Summary: The complementary distance matrix of a graph \(G\) is defined as \(CD(G) = [c_{ij}]\), in which \(c_{ij}= 1 + D-d_{ij}\) if \(i \ne j\) and \(c_{ij}= 0\) if \(i=j\), where \(D\) is the diameter of \(G\) and \(d_{ij}\) is the distance between the vertices \(v_i\) and \(v_j\) in \(G\). The complementary distance energy \(CDE(G)\) of \(G\) is defined as the sum of the absolute values of the eigenvalues of complementary distance matrix of \(G\). Two graphs \(G_1\) and \(G_2\) are said to be \(CD\)-equienergetic if \(CDE(G_1) = RCDE(G_2)\). In this paper, we obtain the \(CD\)-polynomial and \(CD\)-energy of the join of regular graphs of diameter at most two. We use these results to show that there exists at least one pair of \(CD\)-non-cospectral, \(CD\)-equienergetic graphs on \(n\) vertices, for every \(n \geq 6\).