Oh and for anybody who wants to know how to lose weight, it's dead simple, just follow this formula:
Nc = F - (Bmr + E)
Where Nc = Net Calories, F = food calories consumed, Bmr = Basal Metabolic Rate, E = Calories burned during exercise.
The part you left out is Bmr = f(F, Ft, E) where f is a non-linear function that we don't fully understand and Ft = type of Food and is a catchall for the impact of different types of food on your metabolism. A naive reading of your original equation might lead people to assume that Bmr is a number rather than a function of the other variables. A more accurate formula would be:
Nc = F - (f(F, Ft, E) + E)
Also worth noting that F = g(F, Ft, E) where g is a function describing your body's hunger and fullness sensing mechanisms as well the decision making neural pathways in your brain. The ability to solve a differential equation or write an elegant piece of software or make a correct decision under psychologically challenging conditions is very much influenced by F and Ft. So I think your simple equation would be more accurately written as:
Nc = g(F, Ft, E) - f(F, Ft, E) - E
I distributed the subtraction to remove an extraneous pair of parentheses.
Since g and f are non-algebraic functions it's understandable that solving this equation is a bit more complicated than the simplistic arithmetic that your original equation implies.