  In this paper we present a 5-parametric family of static asymptotically flat
solutions for the superposed gravitational and electromagnetic fields of two
Reissner-Nordstr\"om sources with arbitrary parameters -- masses, charges and
separating distance. A procedure for solving of the linear singular integral
equation form of the electrovacuum Einstein - Maxwell equations for stationary
axisymmetric fields is described in detail. The 4-parametric family of
equilibrium configurations of two Reissner-Nordstr\"om sources (one of which
should be a black hole and another one -- a naked singularity) presented in our
recent paper \cite{Alekseev-Belinski:2007} arises after a restriction of the
parameters of the 5-parametric solution presented here by the equilibrium
condition which provides the absence in the solution of conical points on the
symmetry axis between the sources.
