In this work, the exchange energy J for a system of two laterally-coupled quantum dots, each one with an electron, is calculated analytically and in a detailed form, considering them as hydrogen-like atoms, under the Heitler-London approach. The atomic orbitals, associated to each quantum dot, are obtained from translation relations, as functions of the Fock-Darwin states. Our results agree with the reported ones by Burkard, Loss and DiVincenzo in their model of quantum gates based on quantum dots, as well as with some recent experimental reports.