This challenge tomb is a 2-3 coop but is not needed if playing the in-game Nightmare.
Keep going forward until you can anymore as either way is fraught with peril (lol).
I've played it more times that I can count, so go forward.

i completed it solo, just requires a fair bit of back travel

If you're at the crane platform...
#1 Pull the crane using the giant lever attached to it. use the spool of rope next to it so hold it in place with a rope arrow.
#2 Jump across to the other side using the hanging crane platform
#3 Jump to your left and look for the spinning spool below you.
#4 Look across to the other side of the chasm, might need to zoom
#5 attach the spinning rope spool to the rope spool on the other side, in the back of the cave. Wind it in
#6 Climb up the wall to your right (when facing the chasm), jump onto the crane platform in it's new position.
#7 Time your jumps carefully to reach the end.

i completed it, but i couldn't go back. there are two waysto reach the end. one on the left and one on the right.

I too have got to the crane.

Moving the crane does not bring the box to the correct position as described by Cat's Meow.

The rope from the crane to the box is not vertical and so the box only moves out from the wall and not round to the gap. This seems to be the case from the 1st time I saw the rope to the box.

I have tried playing the the entire section again and still have the same problem.

I found a work around, for anyone with the same problem.
#1 Pull the crane as far round as possible and tie off.
#2 Jump from the left corner of the ramp up from the arm on the crane's base. Press [e] when jumping and rope down to the ledge under the winch.
#3 Climb up and use the winch.
#4 The box is still not in the right place but jumping to the drum and failing cures the error after Lara respawns.

I also got stuck at the crane, dug into Reddit and forums and found the actual way out -- there is a climbable ledge in the room next to the crane (with a mural and the door that closes too fast to get through). You have to jump from the plank (right side) to get there
The ledge is a bit to the left of the mural; it's painted white VERY faintly. Then climb onto the wooden beam and you can jump through the hole above the door.

The DLC tombs are quite frustrating, the lack of QA/testing is really apparent.