Histopathology tissue samples are widely available in two states: paraffin-embedded unstained and non-paraffin-embedded stained whole slide RGB images (WSRI). Hematoxylin and eosin stain (H&E) is one of the principal stains in histology but suffers from several shortcomings related to tissue preparation, staining protocols, slowness and human error. We report two novel approaches for training machine learning models for the computational H&E staining and destaining of prostate core biopsy RGB images. The staining model uses a conditional generative adversarial network that learns hierarchical non-linear mappings between whole slide RGB image (WSRI) pairs of prostate core biopsy before and after H&E staining. The trained staining model can then generate computationally H&E-stained prostate core WSRIs using previously unseen non-stained biopsy images as input. The destaining model, by learning mappings between an H&E stained WSRI and a non-stained WSRI of the same biopsy, can computationally destain previously unseen H&E-stained images. Structural and anatomical details of prostate tissue and colors, shapes, geometries, locations of nuclei, stroma, vessels, glands and other cellular components were generated by both models with structural similarity indices of 0.68 (staining) and 0.84 (destaining). The proposed staining and destaining models can engender computational H&E staining and destaining of WSRI biopsies without additional equipment and devices.