I cannot remove the email from my khan academy account. What should I do?

There is an email on my Khan Academy account that I cannot completely get rid of, since it is the only email I can use to log in. But the issue is, that email is already deleted because it was a school email I used to make an account. But it has been 4 years since ever the email was created and I have already transferred to a new school. Plus, there's no password built into the account. What should I do? If I hit "Log out", I'll lose this account forever.