This log is redundant - there is a complete Full Adder which uses this circuit at https://hackaday.io/project/160177-alu-in-dctl-technology/log/150451-full-adder and that work predates this and is more complete.
But, for the sake of not deleting valuable comments below, here it is (for now).
Addition can be decomposed into a carry chain (see past and future logs) and a three input exclusive OR operation which takes the two external inputs and the carry and produces the result.
https://hackaday.io/project/8449-hackaday-ttlers/log/150147-bipolar-xor-gate-with-only-2-transistors is the place to start for all things XOR. I'm just cascading two XOR in the same way as https://hackaday.io/project/160177-alu-in-dctl-technology/log/150451-full-adder and tweaking a few things.
The left hand side a typical BJT set up, some current sets a bipolar transistor to conduct or not, in which case either A is near ground or is wired to the +ve supply via a resistor. I've put it in to show that this is the input we need and also because it was what was needed to help me understand what is going on.
The output has the same characteristics as the left hand side, it's either to ground via a couple of BJT or to +VE via the resistor. I used 330 Ohm resistors, these being slightly faster than 10k. The BJTs are 2N3904s. Currently I'm getting just over 500 kHz, which is good enough.