Pull the decorative plastic trim panel off one of your roof vents (four screws hold it in place). Once you do that, you can see the roof membrane stapled to the framing (where they cut an X in the membrane to install the roof vent).
Pull one of the staples from a flap and inspect the membrane.
If it is black on the back with a white coating on the surface, it's EPDM.
If it is white on BOTH SIDES it is TPO.
If it has a "fuzzy cloth backing" and is white on the top, it's an older version of TPO. (treated just like the new type TPO).
There are other places to inspect the membrane, but the roof vents are, on most trailers, the easiest place to access both sides of the roof membrane.