I'm sorry, it seems not to be impossible to recover your account.
Here is an extract of the above article:
Unfortunately if, when you created the account, you have not registered a secret question which you remember, an alternate recovery email address or phone number to which you have access to receive a reset code, you cannot prove that you are the account's legitimate owner. Hence account recovery is absolutely impossible and there is no way around it.
But, you can report your hacked account to Facebook.