There is no way to get user email using Twitter API. You need to ask user to give his email in your application directly.
You can try to simplify OAuth2 dance using implicit flow feature. See these links for more details:
- OAuth2: the Implicit Flow, aka as the Client-Side Flow
- Google Accounts: Using OAuth 2.0 for Client-side Applications
But I am not sure that you can do it without any redirect at all. From Google link it looks like you have redirect in popup option.
Hope it helps.