Blacklion it sounds like you are using a toolbar that notifies you when you have a new email. Please consider reinstalling the toolbar to reset the notifications. Or if it is for a specific site, check the permissions of notifications for the site:

Right click on the page and click "View Page Info" from the opening menu. This opens a window with a "Permissions" tab. I that, scroll down to the very bottom until you see "Show Notifications" as the third-to-last entry. Either reset that to the default, or just select "Block".

Blacklion said

Windows 7, Xfinity.net webmail. The email notification stopped working after it updated to Firefox 36.0.1. The red numbers that used to appear when new email has arrived does not work any more using FireFox. I check manually now. When I open Internet Explorer the email notification works as before (just fine). How do I turn the red number notification back on, so when email arrives I'll be notified without having to check manually every so often.

I followed your instructions. I unchecked "Show Notifications" then rechecked, reset to default. Problem solved. Thank you.