I managed to pick it up from the text, but only with the aid of a helpful footnote ;)

I've always wondered about this duel myself, because I imagined that Brandon's goal isn't really to kill Willoughby, but rather to get him to marry poor Eliza. I wouldn't expect Brandon to give all the details to Elinor, but I imagine that there was some sort of altercation at the site. Since Brandon pointedly says that they were not wounded, I figure that Brandon was intending merely to scare Willoughby, and probably fired a warning shot. Willoughby, for his part, was probably more wrapped up in the romantic idea of a duel of honor than anything else. Although he's a fine sportsman, I wonder if he would have had the nerve to fire accurately at a man when the time came.