I'm afraid that only Facebook and Microsoft can solve this.
However, if you read David's story here: http://www.zdnet.com/article/locked-out-of-instagram-in-social-space-no-one-can-hear-you-scream and realise that your value for Facebook and Microsoft is a few dollar a year, you can only hope for the best.
Making a new Facebook account (and not forgetting the password of the mail account you for that) seems the most likely way to handle this issue.
Ever thought of using a password manager to safely store all your passwords? I can really recommend it.
When I try to log into my Facebook account I get message that someone recently changed my password (but it wasn't me). I don't have password (new one). Facebook offers me sending new password to my mail address, but I used that mail only for Facebook and don't know mail password anymore (this is @hotmail.com account). Microsoft have option for recovering mail account but it needs a informations of recently sent mails from that account (As I told previously, I used it only for facebook). Can help me with idea for solving this problem?