Looking at both reactions, we can see that the combustion of carbon, graphite or diamond, leads to the formation of carbon dioxide and energy. Since energy is a product of the reaction, we known that this is an exothermic reaction. The value of the change in enthalpy, ΔH, will be negative.
A negative value of ΔH in each exothermic reaction suggests that the carbon dioxide product is at a lower energy than the reactants. And since more energy is released in the combustion of diamond compared to graphite, we know that diamond has a higher internal energy than graphite.