We derive a Hamiltonian for two interacting nucleons starting directly from the Skyrme Lagrangian. Apart from the order-${N}_{c}$ (number of colors) "adiabatic" potential, we find a term of order $\sqrt{{N}_{c}}$ due to the fact that the static two-soliton configuration is not a solution to Hamilton's equations. Using a double expansion in ${{N}_{c}}^{\ensuremath{-}1}$ and the range of the interaction, we show that this term leads to attraction at intermediate range in the scalar channel. The expansion provides a systematic framework for discussing the nucleon-nucleon interaction using solitons. A comparison is made between the soliton approach and the conventional approach based on multipion exchange.