Same caloric input, same exercise (that is, main control signal for caloric output the same). Difference in input is a substance without caloric value. Huge difference in weight.

The only caloric balance here at play is the tautological one ("caloric balance was positive as evidenced by gaining weight. later, caloric balance was negative as evidenced by losing weight"). Other than that, assuming you believe this anecdata (which you may not), the notion of caloric balance is useless.

(And, feel free to disbelieve anything I say, but read on B3 and you'll realize there are numerous reports of reduced weight that starts with B3 supplementation, despite no other change in intake or exercise)