In this paper, we propose a separable reversible data hiding method in encrypted image (RDHEI) based on two-dimensional permutation and exploiting modification direction (EMD). The content owner uses two-dimensional permutation to encrypt original image through encryption key, which provides confidentiality for the original image. Then the data hider divides the encrypted image into a series of non-overlapping blocks and constructs histogram of adjacent encrypted pixel errors. Secret bits are embedded into a series of peak points of the histogram through EMD. Direct decryption, data extraction and image recovery can be performed separately by the receiver according to the availability of encryption key and data-hiding key. Different from some state-of-the-art RDHEI methods, visual quality of the directly decrypted image can be further improved by the receiver holding the encryption key. Experimental results demonstrate that the proposed method outperforms some state-of-the-art methods in embedding capacity and visual quality.