Re: Need a new email after the old one is deleted.
You will have to Call them.
Contact support by phone
If you need help with your account, encounter an error while making a payment, or are unable to log in to the game, please contact the Star Wars: The Old Republic Customer Service team by phone.
Contact our team by calling the numbers listed below:
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For details on how to contact SWTOR support you can follow the steps outlined in this article here: How to get help with STAR WARS™: The Old Republic™
[CM Edit - Edited post to provide an article on how to contact support for STAR WARS™: The Old Republic™ - EA_Illium]