3D multi-object tracking is a crucial component in the perception system of autonomous driving vehicles. Tracking all dynamic objects around the vehicle is essential for tasks such as obstacle avoidance and path planning. Autonomous vehicles are usually equipped with different sensor modalities to improve accuracy and reliability. While sensor fusion has been widely used in object detection networks in recent years, most existing multi-object tracking algorithms either rely on a single input modality, or do not fully exploit the information provided by multiple sensing modalities. In this work, we propose an end-to-end network for joint object detection and tracking based on radar and camera sensor fusion. Our proposed method uses a center-based radar-camera fusion algorithm for object detection and utilizes a greedy algorithm for object association. The proposed greedy algorithm uses the depth, velocity and 2D displacement of the detected objects to associate them through time. This makes our tracking algorithm very robust to occluded and overlapping objects, as the depth and velocity information can help the network in distinguishing them. We evaluate our method on the challenging nuScenes dataset, where it achieves 20.0 AMOTA and outperforms all vision-based 3D tracking methods in the benchmark, as well as the baseline LiDAR-based method. Our method is online with a runtime of 35ms per image, making it very suitable for autonomous driving applications.