Preheat oven to 350 degrees F (175 degrees C).
In a large bowl, combine flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Stir until combined.
In a separate bowl, cream together butter and sugars. Add eggs, one at a time, beating until combined.
Add butter mixture to flour mixture and stir until combined.
Fold in apples and walnuts.
Pour batter into a greased 9x5 inch loaf pan and spread evenly.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Allow to cool in the pan for 10 minutes. Remove from pan and let cool completely on a wire rack.
Drizzle with maple syrup before serving.