We determined theoretically the confined electron states in a colloidal core-shell CdTe-CdS quantum dot system with CdTe as the core material with electron effective mass 0.095 me, CdS as barrier material of electron effective mass 0.25 me and having conduction band offset of 0.265 eV. Based on the one band effective mass approximation, the Schrödinger equation of this system with BenDaniel-Duke Hamiltonian is numerically solved using the finite difference method to obtain the energy level and wave function of the electron confined states. These electronic parameters are obtained by diagonalising the resultant N×N Hamiltonian matrix for principal quantum number n=l – 3, orbital quantum number l=0 – 3 and dot size r=10 – 100 Å. For comparison, we also analytically solve the Schrödinger equation with classical Hamiltonian and similar input parameters to determine the electronic properties. There is good agreement in the results of these two computational methods, where specifically their energy levels differ by less than 15%.