In the Manga
Durham is said to be the greatest gunman that ever lived who can channel his Chi through his precious revolver, allowing him to fire destructive balls of energy without regard to ammunition. His mask also contains a hidden gun in case of emergencies. He heads off to face Train in a part of the story in order to prove that Train is not as great as he sounds. He finds and beats Annette and searches her computer for Train's hideout address, where he finds Eve, whom he beats. He writes a message to Train on the wall, with Eve's blood, for Train to meet him at a forest near the town they are currently in. He is killed by Creed for his selfish insolence, by challenging Train to a gun duel. Durham's Tao Power is called "Shot". His death triggers the exit of Charden and Kyoko from the Apostles of The Stars.

In the Anime
The same as in the manga, except that when he heads off to face Train, he does not torture Annette or Eve. Because of this, he is a more sympathetic character in the anime.

(Source: Wikipedia)