For any chemical reaction, the enthalpy of reaction ($\Delta H$) is the difference between the activation energy of the forward reaction ($E_a$) and the activation energy of the backward reaction ($E_{a(\text{backward})}$):

$\Delta H = E_a - E_{a(\text{backward})}$

For an endothermic reaction, the energy of the products is greater than the energy of the reactants, meaning $\Delta H$ is positive ($> 0$). Therefore, $E_a > E_{a(\text{backward})}$.

Since the activation energy of the backward reaction must be a positive value ($E_{a(\text{backward})} > 0$), we can write:

$E_a = \Delta H + E_{a(\text{backward})}$

Thus, the activation energy ($E_a$) must always be strictly greater than the enthalpy of the reaction ($\Delta H$).