In a secret image sharing (SIS) scheme, a secret image is divided into $n$ shadow images. Then, any $t$ or more shadow images can recover the secret image. Different from pure SIS, extended SIS (ESIS) further embeds shadow images into a cover image to generate stego images. In this way, ESIS can be more secure because shadow images are always noise-like images which might arouse suspicion of attackers, while stego images are meaningful images. Furthermore, if both secret image and cover image can be recovered from enough stego images in an ESIS scheme, the scheme is called reversible ESIS (RESIS). This paper utilizes a new secret sharing scheme based on Chinese remainder theorem for polynomial ring to design a RESIS scheme, which uses polynomials over ${\mathbb{F}}_2\left[x\right]$ to divide secret image. Besides, least significant bit substitution technology is employed to hide shadow images and generate stego images. The proposed RESIS scheme can guarantee both the secret and cover image totally lossless reconstruction. Besides, experimental results show that the shadow images have satisfactory quality which is not affected by different cover images.