The tree-level amplitude for the scattering of two gauge particles constrained to move on the two distinct boundaries of eleven-dimensional space-time in the Horava-Witten formulation of M-theory is constructed. At low momenta this reproduces the corresponding tree-level scattering amplitude of the E_8xE_8 heterotic string theory. After compactification to nine dimensions on a large circle with a suitable Wilson line to break the symmetry to SO(16)xSO(16) this amplitude is used to describe the scattering of two massive SO(16) spinor states - one from each factor of the unbroken symmetry group. The amplitude contains a component that is associated with the exchange of a Kaluza-Klein charge between the boundaries, which is interpreted as the exchange of a D-particle between orientifold planes in the Type IA theory. This is related by T-duality to the effect of a non-BPS D-instanton in the Type I theory which is only invariant under those elements of O(16)xSO(16) that are in SO(16)xSO(16).