Yes tomtank I saw your posts but the first law of thermodynamics does still apply, so where do your calories go? The research John Briffa referenced suggested a difference in metabolism of c.300 calories per day by eating very low carb rather than low fat, but this doesn't seem enough to explain the difference in your case let alone Sam Feltham.
Some earlier research here does not support the argument that a high fat diet burns more energy.
However an interesting 2006 study in mice did find that the mice on a 'ketogenic diet' (KD) lost weight despite consuming just as many calories as mice on other diets: 'KD-fed mice had a unique metabolic and physiological profile, exhibiting increased energy expenditure and very low respiratory quotient.... [The] weight [of mice on KD] dropped and stabilized at 85% initial weight, similar to those on [66% calorie restriction]. This was consistent with increased energy expenditure seen. Animals made obese on [high fat/high sucrose diet] and transitioned to KD lost all excess body weight, improved glucose tolerance, and increased energy expenditure.'
The researchers reckoned that the increased energy expenditure was down to the mice on KD being hotter:
I'm guessing your diet is ketogenic tomtank, so does it make sense that you are burning more energy than those around you who are not on a ketogenic diet? More exercise, more fidgeting, being hotter (no really)?
The alternative I think is that you have energy-filled poops? Don't think I can ask you to research that...