If fat is NOT directly caused by [energy in] > [energy out] that does NOT necessarily violate the laws of nature, by the way. For example:
[Ei] - [Eo] = [WC (M+F)]
Ei - energy in
Eo = energy out
WC = weight change
M = muscle change
F = fat change
[WC (M+F down)] = [Ei] - [Eo up]
^ In this explanation fat mass decreases due to less insulin secretion, energy in turn increases; which people experience in a ketogenic state. Fat loss occurs even though calories have not decreased.
[WC (M+F up)] = [Ei] - [Eo down]
^ Explained as fat going up (because you're eating twinkies and coke all day) and in turn you're energy out goes down. You feel more sedentary because even though you are eating the same energy your body is grabbing the first 10% and sending to fat storage, therefore your energy must decrease. The body is prioritizing in this example.
[WC (M+F down)] = [Ei down] - [Eo]
^ A formula that represents a common theory -- that people lose weight eating "atkins" because the food fills them up and they eat less. But think of it reversed; fat is decreasing while eating this way, and that is driving the urge to eat less, the eating less is not driving the fat loss.
[WC (M up+F down)] = [Ei up] - [Eo up]
^ Calories actually increase (from fat and protein) yet fat loss occurs due to less processed carbs, which releases energy (Eo), plus more release of energy from the gym, and muscle increases. Weight stays neutral. I've experienced this, while the laws of nature are preserved it is false to say I increased exercise while decreasing calories.
[Ei down] - [Eo down] = [WC (M+F) no/small change]
^ What many people experience on calorie restriction, reducing food reduces energy. In turn no change to weight, or small short-term change to weight, followed by becoming fatter. We know starving rats doesn't necessarily make them thin, you can reduce Ei and they will remain fat. We know starving/malnourished people aren't necessarily thin either, which would seem to disprove decreasing Ei must decrease fat mass.
So there are many of possible explanations to explore, beyond the classic "eat less exercise more" (which hasn't worked). The original formula is too simplistic and says nothing at all. But if your mind is not locked into "the world must be flat" you are going to ignore everything nature is telling you to the contrary.