Generally, you can confirm roof type by removing an inner fan vent shroud so you can see a cut edge of the material. If it's black on the bottom, likely EPDM. If solid white, TPO. Either way that roof looks to be toast and can be replaced with whatever you want.
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2012 Jayco White Hawk 28DSBH
2016 Ford Expedition EL XLT 4x4 w/ HD tow
It appears to me that someone used a coating that didn't stay adhered. I would scrape it clean and re-inspect, clean everything very well, and then use Henry's 887 tropicool and re-seal all the areas needed with dicor. ~CA
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