We present a system that estimates the direction of arrival of two competing acoustic sources using two closely spaced receivers that form a differential microphone array. The main advantage of the proposed array topology is that null steering can be essentially performed by adapting a set of two scalars. The direction of arrival estimation relies on the successful estimation of the relative delays between the microphone signals using the decorrelation constraint. Processing is performed in real-time by operating on blocks of recorded data. We examine the performance of the system for different block sizes and investigate its robustness in environments of strong multipath reflections where algorithms often fail to distinguish between the true direction of arrival and that of a dominant reflection. The overall performance of the system is compared to the simple omni-directional array topology. The results indicate that the examined framework can track the two directions of arrival adequately.