The aim of this work is to present an analytical solution for ion transport through a homogeneous ion-exchange membrane in the presence of a 1:1 electrolyte. Electroneutrality is assumed to prevail, coupling ion concentrations in the membrane bulk. Stress is put on the use of Lambert's W function to compute an explicit derivation of the concentration profile as well as the electric field and potential profile within the membrane. An expression of the ohmic electrical resistance of the membrane is proposed also. The relation with transport numbers through the whole membrane system including both adjacent diffusion boundary layers is described thanks to the Nernst-Planck-Donnan formalism.