Describe how events in chapter 18 show that Brian has changed during his time in the Canadian wilderness. How would the old Brian have reacted to these events?

The summary of the chapter is fairly straightforward. Brian is at the plane, and he's trying to get the survival bag. He uses the hatchet to get inside the plane, but he drops the hatchet at one point. He retrieves the hatchet, gets into the plane, gets the bag, and makes it back to shore.
This particular chapter is a good chapter to use in order to point out how Brian has changed from earlier in the book. Paulsen doesn't try to hide the change either. In fact, the narration quite explicitly tells readers that even Brian recognizes that he has changed. This is most clearly illustrated right after Brian drops the hatchet into the lake. He's angry that he dropped the hatchet, but he's not angry at the situation. He's angry at himself. He knows that dropping the most important tool for survival was something that his earlier self would have done.

"That was the kind of thing I would have done before," he said to the lake, to the sky, to the trees. "When I came here—I would have done that. Not now. Not now..."
Yet he had and he hung on the raft for a moment and felt sorry for himself. For his own stupidity. But as before, the self-pity didn't help and he knew that he had only one course of action.
He had to get the hatchet back. He had to dive and get it back.

Notice how quickly Brian moves from emotional anger to logical problem solving. That wouldn't have happened before. He would have wallowed in self-pity for much longer, but his experiences have taught him that self-pity isn't helpful. Brian now knows that he has to act.