Once you find an exit on the "browse map" screen, the workaround to find its exit number, is to select the menu choice prepare route, and prepare a route such that you are routed from a departure point on the interstate, to a destination point on a road that it exits onto. After you select prepare route, first set the depart point on the expressway. The easiest way to set the depart point is to use the point on map menu choice, then point to a spot on the interstate. Then, using the same technique, set a destination point on a road that the exit whose number you want know, leads you to. Again, use the point on map menu choice to select the point. Select a point which is just a little ways from the exit. Your TT is now set to instruct you to get off at the exit, in order to navigate from your selected departure point to your selected destination point.
Once you are finished preparing a route with the prepare route feature, go to the main navigation screen, click on the lower right, select details, then browse as text, and in the list of turn instructions look at the instruction for making a turn at the desired exit. It won't read "exit number nn" it will just read (after an arrow showing you which way to turn) "nn [location]" where nn is the number of the exit and location is the final destination of the road that the exit takes you to. That is, it will read, for example, "62 Smithtown," which you can take to mean "take exit 62 to a road that takes you to Smithtown."
If you click on the instruction, you will see a 2d map or 3d map of the place where you need to turn, and a legend in the upper right reading "62 [name of road that the exit takes you to] [one end of road] [other end of road]." (Click on the map to toggle between 2d and 3d).
If you go to show route demo, and your TT has the feature where a computer voice reads the name of any road that you are instructed to turn onto, you will be able to hear the exit number. After first displaying the name of the road that the exit takes you to, the voice will say, for example, "take the exit right, 62, towards Smithtown." You will also see text reading "62 Smithtown," and subsequently, "62 [road name]."
I have occasionally been able to see exit numbers show up on the "browse map," screen, if I do a lot of zooming in and out. They will appear at one or zoom levels or another. This happens rarely though.