I am flying into Atlanta on American Airlines in Concourse T. Next, I have to go to Concourse E to catch a British Airways' flight. Will I have to go through security again when I get to Concourse E? Also, is the subway between concourses fast? I only have an hour and twenty minutes to make the connection.
Yes, there is a train between the concourses. Your time should be plenty to make the connection. I'm not fully sure about the security - my thinking is that you will not have to go through it again. Maybe someone else can confirm.
No, all the terminals are within the secure zone. You can train or walk. Since you are going from essentially the first terminal to the last, definitely grab the train. They are frequent and fast. Assuming your flight is on time you'll be fine.
I'll second what Michael said. When you get down to where the subway is, there's a digital sign over the doors to the subway that will tell you how long until the next one. They come by every few minutes, so even if it's a few minutes before the next one, go ahead and wait. The airport is well marked, so just follow the signs. An hour and 20 minutes should be plenty of time. Be prepared, though, it is the world's busiest airport, so there's always tons of people there.