The reaction ledger must close energy and signed momentum together. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Input and output energies match
The input energy is 100 J plus 100 J, and the output is the same split.
100+100=200
Opposite photon momenta cancel
The photon momenta are 20 and -20 kg m per s, so the total is 0.