Obtaining the interaction energy between two uniformly charged hemispherical surfaces in compact analytical form seems to be an impossible task to achieve under arbitrary conditions. However, we show in this work that one can obtain the interaction energy between two identical hemispherical surfaces with uniform surface charge density for the special condition of them touching each other along the 'equator'. The mathematical solution method that we apply is remarkable in that the bulk of the treatment is analytic with the only drawback of having to rely on knowledge of certain special functions and their properties.