In this paper, we investigate joint resource allocation and power control mechanisms for two-cell networks, where each cell has some sub-channels which should be allocated to some users. The main goal persuaded in the current work is finding the best power and sub-channel assignment strategies so that the associated sum-rate of network is maximized, while a minimum rate constraint is maintained by each user. The underlying optimization problem is a highly non-convex mixed integer and non-linear problem which does not yield a trivial solution. In this regard, to tackle the problem, using an approximate function which is quite tight at moderate to high signal to interference plus noise ratio (SINR) region, the problem is divided into two disjoint sub-channel assignment and power allocation problems. It is shown that having fixed the allocated power of each user, the subchannel assignment can be thought as a well-known assignment problem which can be effectively solved using the so-called Hungarian method. Then, the power allocation is analytically derived. Furthermore, it is shown that the power can be chosen from two extremal points of the maximum available power or the minimum power satisfying the rate constraint. Numerical results demonstrate the superiority of the proposed approach over the random selection strategy as well as the method proposed in [3] which is regarded as the best known method addressed in the literature.