The studies of the cross sections that originate from the collisions between particles are very important on quantum scattering theory because from them it is possible to calculate the properties of the interacting particles, but in several cases we do not know the potential that models the interaction or its shape is very complex. Although, it is possible to obtain the interaction potential using some approaches based on the inverse problem methodology, as of yet there is no analytical method that can be used for this purpose. In this work, a method to solve the inverse problem in elastic collisions is presented and has the advantage that it is only necessary to know the experimental data of the elastic differential cross section for a single energy value. We tested this method with great success in the process of colliding electrons with hydrogen atoms.