Hello,
You will have to modify the log on web parts which are used on your site. The customization shouldn't be too difficult. You just need to check the database entries for the user according to the user name and if this fails, you will try to authenticate the user with the e-mail address. To change a standard web part please check this
documentation. To authenticate an user please check this
code. For more information on the mentioned methods and tables please check
this and
this link.
Best regards,
Boris Pocatko