This paper develops an explicit solution that estimates the location of a stationary source using time difference of arrival (TDOA) measurements of a signal received by a number of receivers that have random error in their positions. The proposed solution accounts for the error from receiver positions, is algebraic, and does not have the convergence problem as in the Taylor-series linearization method. The Cramer-Rao lower bound (CRLB) of the source location estimate in the presence of sensor position error is derived. Simulation results indicate the proposed solution achieves an accuracy close to the CRLB under Gaussian noise.