Combine water, dates, and raisins in a bowl; let stand 15 minutes. Stir in carrot, walnuts, oil, eggs, and egg white. Combine flour, sugar, baking powder, cinnamon, and salt in a large bowl. Add carrot mixture to flour mixture, stirring just until moist. Spoon batter into an 8 x 4-inch loaf pan coated with cooking spray.
Bake at 350° for 1 hour and 5 minutes or until a wooden pick inserted in center comes out clean. Cool 10 minutes in pan on a wire rack; remove from pan. Cool completely on wire rack.