I have this old Facebook account which I happen not to remember the email address and password used in creating this account. How can I get it back?
If you don't know the email address used, there's not much left to do.
But if you could find which one you used, and have access to it, then you can recover your password using this form.
If you had shared your email address with friends in your old Facebook account, you could try to contact some of your old Facebook account friends and see if the email appear in the personal information section.