The problem of determining a scattering potential from scattered field data is addressed within the two integral equation formulation of scattering theory first proposed by Goldberger (1964). The lowest-order approximation within this formulation casts the inverse problem entirely in terms of the Heitler equation which relates the on-shell T matrix directly to the scattering potential. This lowest-order approximation is applied to the case of non-relativistic quantum mechanical inverse scattering from one-dimensional local potentials and is found to yield an exact solution for the case of a one-dimensional delta function potential.