Another term that could be added to energy balance equation
Very much enjoyed the article on the energy balance equation, but there is actually another factor that should be considered. On the energy out you only considered the burning of calories. There is also the excretion of energy products from the body. In the case of ketosis, since the body cannot store ketones, excess ketones are of course excreted from the body in your urine. So those calories in the fat that are converted to ketones and expelled from the body are part of energy out but do not fall into the four energy out terms you used.
This will of course be a small value on the low-fat diet and higher on a low carb diet.