Lower-limb exoskeletons require actuation systems that can provide accurate joint torque control while preserving low mass and encumbrance. Conventional architectures often rely on independently actuated joints and joint-level torque sensors, increasing system complexity and weight. This paper presents a novel differential actuation architecture for hip-knee flexion/extension, enabling cooperative torque sharing between two motors via a linear differential mapping between motor and joint. To compensate for transmission losses, a model-based friction estimation strategy is developed and experimentally implemented, allowing accurate joint torque estimation without the need for torque sensors. The proposed solution is validated on a physical prototype, demonstrating the feasibility of sensorless torque estimation in a differentially actuated hip-knee module of a lower-limb exoskeleton.