I believe it has been reported that T Rex had a very large well developed space in the skull indicating excellent smell ability. I think I read about the capacity to smell rotting carrion that was 20 miles away. Also the long legs enabled rapid travel to a dead body.
According to the Natural History Museum (NY City) the wear and tear on the teeth suggested a carrion eater rather than a predator. They display showed a life-sized T-Rex scavenging a dead herbivore.