Changing the activation energy of a reaction does not change the equilibrium constant. Remember, the equilibrium constant depends on the thermodynamics of the reaction (i.e. it is dependent on ΔG). ΔG is a state function meaning that the difference in free energy between products and reactants is the same no mater what path you take to go from reactants to products.
Ea, however, is a quantity that describes the path you take from reactants to products. However, changing Ea does not change the identify of the reactants and products, so the overall ΔG of the reaction stays the same. Since ΔG is the same, the equilibrium constant must also be the same.