How do you add a T join in to an existing underground drain pipe?
One technique with a little more digging, but not a lot, is to cut out a section of pipe, add 4 elbows to make an offset and put the tee in the offset. 

Depending on what fittings you can get, there are also "saddle" or "snap" tees made to attach by clipping onto the pipe (and drilling a hole, and gluing, typically.)

This assumes that the pipe size is sufficient for the flow from both roofs - otherwise, you might be better off with a new pipe from the new roof right to the tank.