
206 A.2d 821 (1965)
TRANS WORLD AIRLINES, INC., Appellant,
v.
WORLD WIDE AIRLINES, INC., Appellee.
No. 3594.
District of Columbia Court of Appeals.
Argued December 14, 1964.
Decided February 8, 1965.
Warren E. Baker, Washington, D. C., with whom Joseph M. Paul, Jr., Washington, D. C., was on the brief, for appellant.
Clayton L. Burwell, Washington, D. C., for appellee.
Before HOOD, Chief Judge, and QUINN and MYERS, Associate Judges.
QUINN, Associate Judge.
The dispute in this case involves a letter agreement signed by appellee's president and accepted by appellant's director of aircraft sales, which read as follows:
                      "July 1, 1960
  Mr. Joseph W. Allen
  Trans World Airlines, Inc.
  New York, New York
  Dear Sir:
During our conversation of this date we have agreed to purchase L-1049 A Constellation aircraft N-6904C, purchase price to be $490,000.00 and to execute a final Contract of Conditional Sale generally in conformance with the conditional Sale Contract date May 25, 1960 between the California Airmotive Corp. and World Airlines, Inc. Such aircraft to be placed in work with the Flying Tiger Line, Inc. and delivered to World Wide according to committments [sic] and schedules set forth in *822 your agreement of June 20, 1960 with said Flying Tiger Line.
In order that the aircraft be placed in work with the FTL immenently [sic] we are delivering simultaneously herewith our check in the amount of $10,000.00; final contract of conditional sale to be executed within a reasonable period nuterally [sic] satisfactory to both parties.
            World Wide Airlines, Inc.
                 /s/ S. E. Spicher
                By: S. E. Spicher,
                       President
  Accepted:
   TWA
  /s/ J. W. Allen
              Contract not to be binding
              upon TWA until signed by
              the President or Chairman
              of the Board of Directors
              of TWA.
              (initialed) JWA, SES"
The June 20, 1960, agreement between appellant and the Flying Tiger Line provided that the plane would be overhauled, modified, and repainted with appellee's insignia and colors. It further provided that the plane would be delivered to the Flying Tiger Line by appellant on July 6, 1960, and that the work would be completed within forty-five days. Though not a party, appellee's president initialed each page of this agreement and at the end wrote:
"Accepted: By World Wide Airlines, Inc. subject to final contract of Conditional Sale between World Wide Airlines, Inc. and Trans World Airlines, Inc. /s/ SESpicher President 7/1/60"
While the work was in progress, appellant prepared and submitted to appellee a conditional sales contract pursuant to the letter agreement. That part of the contract relating to the purchase price provided:
"The purchase price of the Property is Four Hundred Ninety Thousand Dollars ($490,000) of which Ten Thousand Dollars ($10,000) shall be paid on July 5, 1960, Ten Thousand Dollars ($10,000) shall be paid on July 22, 1960, Ten Thousand Dollars ($10,000) shall be paid on August 1, 1960, Twelve Thousand Dollars ($12,000) shall be paid on August 15, 1960, and the balance of the purchase price shall be paid in thirty six (36) consecutive monthly instalments of Fourteen Thousand Eight Hundred Seventy one and 11/100ths ($14,871.11) each, such instalments to be paid on the first day of each calendar month commencing October 1, 1960. The foregoing instalments include discount interest at the rate of six and one-half percent (6½%)."[1]
In another paragraph the contract recited:
"Solely as an accommodation to Buyer, Seller has entered into an agreement dated June 20, 1960 with The Flying Tiger Line, Inc. under which The Flying Tiger Line, Inc. will overhaul and modify the Airplane. * * *"
*823 The contract, however, was not signed by either appellant's president or chairman of the board of directors. When the plane was tendered for delivery  several weeks beyond the forty-five-day limit  appellee refused acceptance on the grounds that delivery was untimely and that appellant had chosen to remain unbound "even to the present time." Appellant responded by stating it would resell the aircraft and look to appellee for damages for wrongful breach of contract. This suit followed whereby appellee sought recovery of the $10,000 and appellant counterclaimed for damages.
In its memorandum opinion the trial court ruled that there was no enforceable agreement between the parties because neither appellant's president nor chairman of the board of directors had signed the proposed conditional sales contract. Accordingly, appellee was entitled to a return of the $10,000 deposit and a finding was entered against appellant on the counterclaim.
Appellant contends that this ruling overlooks the language in the letter agreement whereby appellee stated it was delivering its check of $10,000  not as a deposit  but "in order that the aircraft be placed in work with FTL immenently [sic]." Appellant urges that the $10,000 was consideration for a unilateral contract in which appellant specially agreed to take the plane off the market immediately and place it in overhaul with the Flying Tiger Line prior to the execution of the conditional sales contract, and that this is the plain meaning of the letter agreement. Secondly, appellant contends that the trial court erred in refusing to receive competent and relevant testimony showing the circumstances surrounding the $10,000 payment. Appellee argues that the $10,000 was a deposit and that the case might have been decided upon motion for summary judgment on the basis of the letter agreement and the related documents.
We have carefully reviewed the letter agreement, the June 20, 1960, agreement, the proposed conditional sales contract, and the other exhibits in the file. A careful reading of all these documents convinces us that parol testimony should have been admitted to explain the understanding of the parties with regard to the $10,000 check.
Taking the letter agreement first, it states that the $10,000 was paid so that the plane might be placed in work with the Flying Tiger Line immediately. It supports appellant's theory that the $10,000 was consideration for a unilateral contract. While the June 20 contract between the Flying Tiger Line and appellant contains no reference to the $10,000, each page thereof was initialed by appellee's president who accepted the contract on July 1, the same day he signed the letter agreement. A reasonable inference to be drawn from these two documents is that when the letter agreement was signed on July 1, appellant also agreed, in return for an additional $10,000, to specify July 6 as the delivery date to the Flying Tiger Line. Further, the conditional sales contract proposed by appellant makes no mention of a July 1 deposit but rather refers to a $10,000 payment on July 5. The check was never admitted or offered in evidence by appellee. Nevertheless, the conditional sales contract also recited:
"Solely as an accommodation to Buyer, Seller has entered into an agreement dated June 20, 1960 with The Flying Tiger Line, Inc. under which The Flying Tiger Line, Inc. will overhaul and modify the Airplane." (Emphasis supplied.)
We hold, therefore, that the case must be remanded to the trial court for the admission of parol testimony. While parol evidence is not admissible to vary or alter the terms of a written contract, it is admissible to explain the terms when there is an ambiguity in the language of an agreement. Dixon v. Wilson, D.C.App., 192 A.2d 289, 291 (1963). Here the documentary evidence is self-contradictory and parol testimony should be admitted to ascertain the true intent of the parties, namely, whether the $10,000 was consideration *824 for a unilateral contract or a deposit on the sale price. If the trial court reaches the latter conclusion, it may then decide whether there was an enforceable agreement between the parties.
Reversed and remanded for proceedings not inconsistent with this opinion.
NOTES
[1]  Pursuant to the letter agreement, these terms were in conformity with the "conditional Sale Contract date May 25, 1960 between the California Airmotive Corp. and World Airlines, Inc." Those terms were:

"The purchase price of the property is Four Hundred Ninety Thousand Dollars ($490,000.00), of which $42,000.00 shall be paid upon the signing of this Conditional Contract of Sale. A Deposit made to Seller by Buyer on May 9, 1960 in the amount of $10,000.00 shall be considered as part of the $42,000.00 down payment and shall be applied against the $42,000. The remaining balance of $448,000.00 shall be paid in Thirty Six consecutive monthly instalments of $14,879.26 each, such instalments to be paid on the first day of each calendar month following delivery of the Aircraft. The foregoing instalments include discount interest at the rate of Six and One Half Per Cent (6.5%)."
