Transfer reactions in inverse kinematics using the radioactive ion beams provided by the REX-ISOLDE facility at CERN are very good tools to gain insight into the single-particle properties of exotic nuclei. The new silicon particle detector setup T-REX, optimized for these transfer reactions, is presented in this article. T-REX consists of position sensitive ΔE-E telescopes in a compact configuration that covers up to 66% of the solid angle. The setup allows the identification of the light reaction products and the measurement of their angular distribution for a large range of polar angles. Simultaneous detection of the elastically scattered target-like nuclei enables the determination of the optical model parameters used in the analysis of the experiments
