It will take you anywhere from 1/4 to 1/2 of the time that it would require in Miami MIA.

If your bags are not checked through, the International Arrivals area in IAH works pretty smooth. You will first need to clear imigration, which is the area where depending on arrival time pax loads will be your biggest variable. I've gone through the visitors (Non US/Green Card) side with family or friends several times and do not believe even at the heaviest of times was in que for more than 20 minutes. After cleared, head down to the glass proa of this ship-looking space and down the escalators to baggage claim. (Do not try to take the stairs hidden on your left down if security forces are around, they do not like that for some reason?????)

If your bags are not already on the belt when you get there, they usually will be within 5 minutes, use a free cart if needed and load up and wheel down to customs at the far end of the baggage area. I have never seen lines in this area longer than a minute or so as they usualy have 3 lines going and pop you out to the bag recheck area. Again very seldom lines here and after rechecking your bags the escalators/allowed stairs back up are on your left. At the top you are now magically in Term D international arrivals TSA security screening area, where there indeed is a Elite line that sometimes is respected by the TSA agent running herd over the masses that arrive. 5-15 minutes here and out you go to the D terminal, turn left and follow the flow over an enclosed bridge and you will come right to the Term E PC lounge right in front of you. There, depending on your departure gate turn right or left.

In the last 10 times I did this (albeit not a Int-Int connection but rather Int-Dom) the total time has varied from 10 minutes to about 30 minutes. YMMV, but usually the tighter your connection the slower the process. If you have over 1-1/2 hours it is even possible to have some time in the PC and even head down to E-4 for food at Pappadeux.