You can accomplish this using our push notifications (http://support.membermouse.com/knowledgebase/articles/319066-using-push-notifications). You would just create a script that's called on the 'Member Account Updated' event and in this script you can check if the email was changed by comparing the last email to the current email.
The last email is stored in $_GET["last_email"]
The current email is stored in $_GET["email"]
You'll also find this and more info in the sample script that you can download here: https://support.membermouse.com/a/solutions/articles/9000020278-call-a-custom-script-when-certain-events-occur