Water damage on a travel trailer is kind of like rust on an old car (two things I'm very familiar with). The evidence you see is only a small part of the damage behind it. Check the rubber roof and you'll probably find it to be soft above this area. If you seal the edges, you'll just be sealing in the moisture and any rotted wood inside, but if you don't seal it, more water will get in and continue the process.
Dealing with it depends on what you are willing or able to do. If you have to pay someone else to do the work, it will be expensive. If you have the ability to do it yourself, you will trade time for money. I think you'll have to remove the edge moldings and peel back the rubber roof to expose the damage and replace the rotted wood. But be prepared, because as I said, there is always more to be replaced than you can see on the outside.
Much depends on what your plans are for this camper, but you're not alone, this is a common issue with these trailers and much has been documented on this site concerning the repair process.
Wishing you the best,
1992 T-2470 (now residing in South Carolina)
Current Sunline-2007 Solaris 2499
2018 Silverado 1500 w/Max Trailering pkg.