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 $$R\gg r,$$ R≫r, up to the term quadratic in the ratio r / R. The consideration proposes the law $$a+b R^{1/3}$$ a+bR1/3 for the energy, when the charges are close to one another, $$R\rightarrow 0$$ R→0 . This leads to the singularity of the force between them to be $$R^{-2/3}$$ R-2/3 , which is weaker than the Coulomb law, $$R^{-2}$$ R-2 .