The discovery of a plume of water vapour and ice particles emerging from warm fractures (`tiger stripes') in Saturn's small, icy moon Enceladus raised the question of whether the plume emerges from a subsurface liquid source or from the decomposition of ice. Previous compositional analyses of particles injected by the plume into Saturn's diffuse E ring have already indicated the presence of liquid water, but the mechanisms driving the plume emission are still debated. Here we report an analysis of the composition of freshly ejected particles close to the sources. Salt-rich ice particles are found to dominate the total mass flux of ejected solids (more than 99 per cent) but they are depleted in the population escaping into Saturn's E ring. Ice grains containing organic compounds are found to be more abundant in dense parts of the plume. Whereas previous Cassini observations were compatible with a variety of plume formation mechanisms, these data eliminate or severely constrain non-liquid models and strongly imply that a salt-water reservoir with a large evaporating surface provides nearly all of the matter in the plume.