This paper proposes a fully homomorphic encryption encapsulated difference expansion (FHEE-DE) scheme for reversible data hiding in encrypted domain (RDH-ED). In the proposed scheme, we use key-switching and bootstrapping techniques to control the ciphertext extension and decryption failure. To realize the data extraction directly from the encrypted domain without the private key, a key-switching based least-significant-bit (KS-LSB) data hiding method has been designed. In application, the user first encrypts the plaintext and uploads ciphertext to the server. Then the server performs data hiding by FHEE-DE and KS-LSB to obtain the marked ciphertext. Additional data can be extracted directly from the marked ciphertext by the server without the private key. The user can decrypt the marked ciphertext to obtain the marked plaintext. Then additional data or plaintext can be obtained from the marked plaintext by using the standard DE extraction or recovery. A fidelity constraint of DE is introduced to reduce the distortion of the marked plaintext. FHEE-DE enables the server to implement FHEE-DE recovery or extraction on the marked ciphertext, which returns the ciphertext of original plaintext or additional data to the user. In addition, we simplified the homomorphic operations of the proposed universal FHEE-DE to obtain an efficient version. The Experimental results demonstrate that the embedding capacity, fidelity, and reversibility of the proposed scheme are superior to existing RDH-ED methods, and fully separability is achieved without reducing the security of encryption.