The two equations to solve are boxed in pink. The first one is for the currents at the Y node. The second is for the second transistor's emitter current. (When we did it in Excel, I think we used the collector current, but in this case, with the forward active assumptions, you don't get the collector voltage independently of the collector current).

As for the second equation

I haven't tried to really solve those equations, like with an HP50g -- too complex. But I verified that they are approximately satisfied by the known solutions.