What sort of computations are used for localising sound with the ears, and how does the brain compute the time difference between sounds reaching each ear? I am interested in the specific mechanisms rather than a general account.
From the physics(acoustics) perspective, the sensory input changes depending upon pitch. When you hear a sound that is high-pitched, your head blocks the sound wave, creating a sound shadow for the ear on the opposite side of your head from the sound source. This sound shadow means that your ears hear the sound at two different volumes, which the brain then uses to calculate direction.
For low-pitched sound, the distance between your ears creates a phase difference between the sound perceived in each ear. And that phase difference indicates sound direction. If I understand your question, it centered upon the brain's processing of this phase difference information.
For mixed-pitch sounds, you utilize both, which makes complex sounds even easier to locate.
Some neuroscience papers on sound localization: