While editing theme's functions.php file an error occurred and I've lost the access to theme editor, cause the site was down.
I don't have logins for FTP or cPanel. Is there anyway to recover the site only with WordPress logins?
If you don't have FTP or cPanel then I guess you don't have ssh access too. If your hosting service provider offers ssh access then you can try that. Otherwise, I'm afraid there's no way!