A Request was made for a book with two ISBNs -  ISBN-13: 9780226307787 and ISBN-10: 0226307786.

My posted book has ISBN-10: 0226307786.  It has the same title, n=but different cover than requested item with 2 ISBNs.

The Requestor's condition is that the posted book must match the ISBN.

I do not want to  mislead the Requestor, but do not know how to get in touch to ask him if my posted book is acceptable.

Any suggestions would be appreciated.

As long as your ISBN-10 number matches the requested ISBN-10 number and  the title, author, and binding match (e.g., paperback, hardback), you may send the book. The cover does not need to match. You do not need to PM the requestor.

The 13 digit ISBN is the expanded version of the 10 digit ISBN. It's the same number except a prefix of 978 was added and the last digit was changed in order to convert it to the new numbering system. (I'm not sure why the last number was changed. It would probably be easier to understand if the last digit stayed the same and a just the 3 digit prefix was added.)

The last digit of any ISBN (either 10 or 13 digits) is called a check digit, and it can be calculated by applying a formula to other digits in the number. This way, a computer can easily check and see if there is a typo in the number. It just applies the proper formula and checks to see if it gets the last digit as the result. If not, then it knows there's something wrong with the number.

When we were running out of 10-digit (really 9-digit) ISBNs, and they decided to expand to 13-digits, the same prefix was added to every one. Since the formula to calculate the check digit now has to apply to the first 12 digits of the number, instead of the first 9 digits, the last number also changed. Eventually, when the 10-digit numbers run out, books will only have 13-digit ISBNs and they will start with something other than 978.

It's the same book. Sometimes they put both numbers on the back sometimes they only put one.  The 978 is probably inside the book on the publishing info page. 

The last digit of any ISBN (either 10 or 13 digits) is called a check digit, and it can be calculated by applying a formula to other digits in the number.

Makes sense. Thanks for the info.