Massive machine-type communication (mMTC) is a newly introduced service category in 5G wireless communication systems to support a variety of Internet-of-Things (IoT) applications. In recovering sparsely represented multi-user vectors, compressed sensing based multi-user detection (CS-MUD) can be used. CS-MUD is a feasible solution to the grant-free uplink non-orthogonal multiple access (NOMA) environments. In CS-MUD, active user detection (AUD) and channel estimation (CE) should be performed before data detection. In this paper, we propose the expectation propagation based joint AUD and CE (EP-AUD/CE) technique for mMTC networks. The expectation propagation (EP) algorithm is a Bayesian framework that approximates a computationally intractable probability distribution to an easily tractable distribution. The proposed technique finds the best approximation of the posterior distribution of the sparse channel vector. Using the approximate distribution, AUD and CE are jointly performed. We show by numerical simulations that the proposed technique substantially enhances AUD and CE performances over competing algorithms.