Equality constraints are common in robotics, arising in applications such as pose-constrained manipulation, coordinated motion, and task-space planning. Classical constrained planners typically assume an analytic constraint function, whereas in practice only feasible demonstrations may be available. We study how to learn explicit equality constraints directly from such demonstrations. We propose Orthonormal Neural Constraint Learning (ONCL), a method that learns multiple scalar constraint functions jointly and represents the equality constraint by their common zero set. Rather than estimating local normal directions and generating large amounts of supervised off-constraint data as related works, ONCL regularizes the gradients of different constraint functions to be normalized and mutually orthogonal, inducing a structured local normal space during learning. This yields an explicit differentiable constraint model in the original state space for evaluation and downstream planning. We evaluate ONCL on ten synthetic and robotic datasets spanning dimensions from 2 to 12. ONCL significantly outperforms each of three baselines on six datasets, while remaining competitive on the other datasets. We further validate ONCL on a physical KUKA iiwa 14 using kinesthetic demonstrations collected by a human operator. The learned pose constraint is subsequently used on the same platform for downstream trajectory planning under a modified task objective and an additional known obstacle-avoidance constraint.