I have just had the same problem but didn't want to have to delete my email account and set it up again.

So instead of holding on the email and then clicking delete try holding on the email but then click "select more" then only select the one email causing the problem, then click delete - This worked for me.

This seems to be a common problem with the Z10. The only solution that worked for other users was to delete the email account then add it again. Those email shouldn't appear anymore.

Let me know if this solution also works for you.