Depends on how far down the shaft has broken... you may be able to grab it with some pipe grips if you're lucky.
Failing that, strip the other side, get a length of flat steel bar, or studding... with the aid of a torch and some jiggery pokery, you should be able to thread the bar through the diff (if it's a 2 pinion diff then there will be a pin across the middle of the "hole" that you need to get the bar past, if it's a 4 pin diff, or an ARB locker type diff, then there's no pin across the middle, just a large halfshaft-diameter hole, so you can use a beeft length of bar, and smack the broken piece of shaft out (with a hammer on the end of the bar! :dance:)