LoRa is a popular low-power wide-area network (LPWAN) technology that uses spread-spectrum to achieve long-range connectivity and resilience to noise and interference. For energy efficiency reasons, LoRa adopts a pure ALOHA access scheme, which leads to reduced network throughput due to packet collisions at the gateways. To alleviate this issue, in this paper we analyze and implement a LoRa receiver that is able to decode LoRa packets from two interfering users. Our main contribution is a two-user detector derived in a maximum-likelihood fashion using a detailed interference model. As the complexity of the maximum-likelihood sequence estimation is prohibitive, a complexity-reduction technique is introduced to enable a practical implementation of the proposed two-user detector. This detector has been implemented along with an interference-robust synchronization algorithm on the GNU Radio software-defined radio (SDR) platform. The SDR implementation shows the effectiveness of the proposed method and also allows its experimental evaluation. Measurements indicate that our detector inherently leverages the time offset between the two colliding users to separate and demodulate their signals.