Connecting flight at IAH

Hi. Hope this is the right subreddit for this question.

I have a connecting flight at IAH. Flying in on United and flying out on Mesa airlines dba united express.

The layover is 30 minutes. I think I read that Mesa flies out of terminal E. Will I have to catch my connecting flight if I fly into terminal A, B, C or D? I know I’ll have to change terminals because united told me after I booked the ticket.

Thanks for your help.