A neural network, originally proposed as a model for nuclei in the auditory brainstem, uses gradients of cell thresholds to reliably compute the difference of inputs over wide input ranges. The encoding of difference is linear even though the individual components of the network are finite, saturating, nonlinear devices highly dependent on input level. Theorems are proven that explain the linear dependence of network output on difference and that show the robustness of the network to perturbations of the threshold gradients. There is some evidence that the network exists in the neural tissue of the auditory brainstem.