I'm assuming that Admin is your default account and that it is an administrator account. If it is an administrator account it will say "Admin" in small letters below the main "Admin" name. If you click the i it will say "allow this user to administer this computer" and the switch will be on but greyed out. If it's not an Admin account or it's not your main account then don't delete or change anything and come back here.
Assuming Admin is an admin account then the best thing to do is to log in to the other Admin-with-email account and see what's in there. If you don't know the password then you can reset it by clicking on the i link. If there are any files that you want to keep then you can copy them to the other Admin account by dropping them in its "Public" folder (HD/users/Admin/Public) or you can transfer them via external storage - up to you. Note that if you drop stuff into Admin's Public from Admins-with-email account you'll have to change their permissions when you log back in as your main Admin account. Google or come back here for help if that's an issue.
After you're happy there are no files, music, ,movies, pictures, etc in the admin-with-email account then you can delete the Admin-with-email account.
DON'T DELETE ANYTHING IF YOUR MAIN ADMIN ACCOUNT ISN'T AN Admin account.