$${\Delta E = E_2 - E_1 \\ = \frac{-(13,60\, \mathrm{eV})(Z - 1)^2}{2^2} - \frac{-(13,60\, \mathrm{eV})(Z - 1)^2}{1^2} \\ = (10,2\, \mathrm{eV})(Z - 1)^2}$$