The calories out is mostly your body surviving. You can just ignore all exercise to simplify the out portion. You can get your BMR tested close enough that you can work with it. Or, you can estimate and iterate.
Tell me how calories, legally, are measured in food. Also, tell me the caloric value (legally, as per FDA regulation) of butyrates.
When you understand why I asked those two questions, then that will answer your question far better than me spending a dozen pages to answer you. The statistics available to the average consumer are not a level playing field.
Even if we do not know the true energy content of a particular food item, we know that the amount ingested is proportional to the energy intake. At that point, we need only a simple bisection search algorithm to find a point which allows weight loss without an excessive (note: not zero) feeling of hunger.
