Is it possible to restore my private msgs

The reason is because i once bought an starcraft 2 account on the black market but i cant remember the e mail adress

and so i cannot log in i kno its in a old private msg any chance to recover?

write a private message to an admin and try your luck.

The best way to go would be as Drew has stated, we can't promise that you can recover them, as they are deleted for a reason, yet, if any, the best way would be by contacting any administrator and hope it will be possible.