I'm flying from ORD to LIR on United (CO operated) and have a connection through IAH. I've never flown into IAH and have no idea what to expect, but 39 minutes is pushing it for me regardless of how well I know the airport. Also concerned with needing to change terminals for international?

Looking at the map of IAH i see CO flys into C and E, and it seems like E is the international? Is this connection even possible?