Which one needs longer runway of an airplane between take off and landing for a constant weight? Consider we have an airplane that the weight will be constant when take off and landing (in fact will be no such common airplane right now as the fuel will be less due to engine consumption. But in an electric airplane, that will be possible, I guess). What I am asking is, which one is required longer runnway from an airplane starts taking off in the edge of the runway until it just leaving the runway (ground), compared to when that airplane is landing, from it start touching the runway until it can stop safely in the runway. How do we calculate the required runway for landing?
Generally, aircraft require longer distance for taking off than landing roll. 

The standard definition for take-off phase is from the start of acceleration (stopped aircraft) to the point where aircraft reaches 35 ft above ground. Similarly, the landing phase is from 35 ft to the final stop. What you mentioned is a sub-phase, which is called "ground roll".

When the aircraft is accelerating for the take-off, the engins' thrust must overcome the aerodynamic drag and the ground friction, and the resultant will contribute to the acceleration. But when the aircraft is landing the reversed thrust in addition to an increased aerodynamic drag (due to spoilers and increased flap deflection) and increases ground friction (due to application of brakes) are decelerating the aircraft. This is physical reason.

While there are some engineering methods (such as equations or charts, usually presented in aircraft design books i.e. Roskam or in aircraft performance books), the most accurate method is to writing the force balance acting on the aircraft and computing the acceleration at any time step, and solving the position differential equation for the distance. But this method requires details about aerodynamic and thrust characteristics. This method somewhere was called time marching.