We consider two point-like charges in electrostatic interaction within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a dipole-like approximation, where the separation between them R is much smaller than the observation distance r : with the linear accuracy with respect to the ratio R/r , and in the opposite approximation, where R r, up to the term quadratic in the ratio r/R. The consideration proposes the law a + bR 1/3 for the energy, when the charges are close to one another, R → 0. This leads to the singularity of the force between them to be R −2/3 , which is weaker than the Coulomb law, R −2 .