For a reaction for which the activation energies of forward and reverse reactions are equal, then both $∆\mathrm{H}$ and $∆\mathrm{S}$ are 0.
The activation energy is the energy it takes to push the reactants up to the transition state.
For Exothermic reaction = negative $∆\mathrm{H}$
Endothermic reaction = positive $∆\mathrm{H}$