Energy balance is the difference between the energy you take in from food and the energy you burn. If it is positive for weeks, you gain weight (calorie surplus). If it is negative, you lose weight (calorie deficit). If it is balanced, you maintain.
What is on each side
On the intake side are the calories from protein, carbohydrates, fat and alcohol. On the expenditure side is your total daily energy expenditure: basal metabolic rate, everyday movement, training and digestion. This balance decides whether you gain, lose or maintain. Which diet you use is secondary, as long as it reliably creates the balance you want.
From calories to kilograms
To convert, the usual approximation is about 7,700 kcal per kilogram of body weight. It is not a fixed constant: how much energy a kilogram of change contains depends on how much of it is fat, muscle and water (Hall 2008). It is still good enough for steering.
Example: You keep a deficit of 500 kcal per day from Monday to Friday, so 2,500 kcal. On Saturday you eat 3,000 kcal above your needs. Your weekly balance is now slightly positive and the deficit is gone. These numbers are a worked example.
Why the scale does not show the balance
In the short term, water, glycogen and gut content mask your energy balance. A one-kilogram jump overnight is practically never fat, because that would take a surplus of several thousand calories. The balance only shows up in the slope of your trend weight over two to three weeks. You can also run it backwards: your intake plus your trend change tells you what you actually burned.