High-energy gamma-ray and neutron emission from the 2003 October 28 solar flare was observed by RHESSI, CORONAS and Integral and by the Tsumeb neutron monitor. Relativistic electron bremsstrahlung, nuclear deexcitation gamma-ray lines and continuum, the 0.511 MeV positron-annihilation line, the 2.223 MeV neutron-capture line, pion-decay emission, and neutrons were observed. Solar energetic particles accelerated by a shock associated with a coronal mass ejeciton (CME) were also observed in space and by ground-based monitors. This remarkably-wide range of observations offers a unique opportunity for studying ion acceleration. We review the high-energy emission theory and the procedure developed for analyzing such flare data. We discuss the results of applying the procedure to the October 28 flare data, and argue for the presence of two components of energetic particles producing the flare emissions, one accelerated by the flare itself and one accelerated by the CME-associated shock.