Clock synchronization among the nodes of Wireless Sensor Networks (WSN) is important for many of its applications but this task becomes quite complex due to their special characteristics. To achieve this goal of clock synchronization, there have been many protocols and algorithms presented so far all of which rely on some kind of timing message exchange among the nodes to be synchronized. In this paper, we have derived the Maximum Likelihood Estimates (MLE) for clock offset and skew for a two-way timing message exchange mechanism where the deterministic portion of timing delays, e.g., transmission, propagation and reception times, etc., are known at the receiver or are assumed to be equal to 0. A similar methodology can be applied to derive the ML estimates for other message exchange mechanisms. An algorithm to estimate these clock parameters in this case is also presented in detail.