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A majority of traffic engineering techniques aims to minimize network congestion in SDN, but they commonly have considered some aspects of the flows and their demands for evaluating applications in SDN. This paper focuses on a scalable traffic engineering scheme for efficiently mapping traffic demands to paths in SDN datacenters. In this regard, an optimal solution is introduced to schedule elephant flows across paths to mitigate network congestion and increase load balancing in SDN. Nevertheless, optimal flows scheduling mechanism is still not applicable because the required time to calculate the optimal paths is not tolerable in SDN. We present a new decomposition technique for limiting the search space based on the linear programming method to solve the problem in a reasonable time. Since the mice flows have the sensitive time requirements, some paths are reserved for immediately forwarding these flows. The proposed method achieves reasonable performance regarding computation time compared with state-of-the-art solutions devoted to this topic. The results also show that the proposed traffic engineering method is effective to control network congestion and provide load balancing in SDN datacenters. [ABSTRACT FROM AUTHOR]