A method for separating a mixture of solid materials can includes a sorting step based on differences in X-Ray transmission of different materials and a density sorting step at an elevated density. The mixture of solid materials can be a plastic-rich mixture recovered from waste electrical and electronic equipment. The mixture of solid materials can include plastics that contain brominated flame retardants. In some cases, a XRT or DEXRT sorter is used to remove the majority of plastics that contain brominated flame retardants from the mixture.