In a large bowl, beat the eggs, oil and sugars until smooth. Combine the flour, cinnamon, baking powder, baking soda and salt; gradually add to egg mixture just until combined. Stir in carrots and apple.
Spoon into a greased 9-in. square baking pan. Bake at 350° for 25-30 minutes or until a toothpick inserted near the center comes out clean. Cool on a wire rack.
In a small bowl, combine the frosting ingredients; beat until smooth. Spread over cake. Store in the refrigerator. Yield: 9 servings.