35 minutes between connections on Newark airport

Things you should calculate yourself, Considering the changes in a scenario which may occur surprisingly.

It should be single booking, (Code-sharing by Air-Line is fine)
The gates should be close enough, and you need to take an intra-airport transport.
Your first flight should not be delayed. In such cases, the airlines give you the other options for single bookings. But if you have not done the single booking, it will cost you to book another flight.
In case you reach a bit late, they may ask you to run. So be ready for that.

Hope this helps.

If your inbound flight is on schedule... and you run... you'll probably be fine. You may not even have to run, if your gates are close together.

If anything goes wrong, it is extremely likely you will miss your connecting flight.

Jim MacKenzie 15330

Source: stackoverflow.com