Pre-flop - nothing different here, you don't seem to have enough to raise b/c you are OOP.

Flop, you bet and he calls. I like the size of your bet here, but maybe a little higher in the same range. If he had two pair, A-anything, I think he would raise to test his hand on that board. The other possibility is he is slowing playing the nuts, or a a draw to it. Thus, I see you ahead of villian on this flop.

Turn: If he has the ten you're stuck, but with your flop bet and turn check, if he has the str8 now or had it before, he knows you are scared of it now. That means he either checks or raises a callable amount. If he had AK, I think he would probably bet, again because he just made his hand and he had no info on where he stands with Broadway on the board. At this point, I see it as villian doen not even have TP or he has the nuts.

The turn is a good spot to bet. If you bet here, if he smooth calls fast, I would put him on the str8. If he doesn't have a ten, two pair or an A he should fold. Someone below recommended t90, that's fine but if he is as loose as you think, then you may want to go a teeny bit higher, especially at a $10+1. This is a good place to bet, because if he does not have the str8, he should fold, if he calls, you can feel more comfortable w/ a check/fold on the end.

River is a brick: All-in is stupid here, b/c he only calls if he has a ten or two-pair and doesn't believe you. Either way, if he calls it's lights out for you or a split pot. Not betting on the turn, really hurt you b/c you don't have any more info re: the Broadway staring you in the face. A check could might encourage him to push at you, so I would probably put something in the pot b/c your kicker won't play and maybe he folds with Kx, Qx or Jx. He might even call with those, which is good for you.