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I understand from your post that you have deleted your email account but when adding it back to your iPhone you receive a message saying it is already added. Verify that your email account has been removed under Settings > Mail > Accounts (If you're using iOS 11 or later, go to Settings > Accounts & Passwords). Then force quit the Mail app and restart your iPhone. The following articles will provide you with the steps to force quit apps and restart your iPhone:
How to force an app to close on your iPhone, iPad, or iPod touch - Apple Support
Restart your iPhone, iPad, or iPod touch - Apple Support
If the issue persists and you are still unable to add your email account to your iPhone, you may need to contact your email server provider for additional assistance.