Hi Sandra,
Recipe from Cooking Light magazine in an ad for Second Nature Eggs.

Cranberry-Orange Carrot Cake

1 box spice cake mix 2 cups grated carrots
1 cup water 1/2 cup dried cranberries or golden raisins
1/3 cup applesauce 2 tsps. grated orange peel
3/4 cup Second Nature Eggs (equivalent to 3 eggs)

Heat oven to 350 degrees. Prepare 8 or 9 inch cake pans with cooking spray. Combine cake mix, water, applesauce and eggs in large mixing bowl. Beat on low speed 1 minute; continue beating on medium 2 min. Stir in carrots, cranberries or raisins and orange peel. Pour into prepared pans and bake for 30-35 min. until toothpick inserted in center comes out clean. Cool 10 min. Turn out onto rack and cool completely.

Frost with Orange Cream Cheese Frosting

For easy Carrot Cake recipe does say omit cranberries, raisins and orange peel