Place the water, salt, white sugar, flours, and yeast into a bread machine pan in that order. Turn the bread machine to the dough setting and push start.
Once the dough cycle has completed (mine lasts 1 1/2 hours). Deflate the dough and turn it out onto a lightly floured surface. Roll the dough into a rectangle then fold in half and seal the seam firmly with the side of your hand. Roll up dough jelly roll style very tightly and pinch the seam closed really well. Place the loaf onto a silpat mat that has been sprinkled with cornmeal. Cover with a cloth and let rise, until doubled in size, about 40 minutes.
Preheat the oven to 375 degrees. Combine the egg with the water and beat until thoroughly mixed. Brush the egg mixture on the top of the loaf. Carefully slice three diagonal slits across the loaf with a very sharp knife. Place the silpat mat onto a baking sheet.
Place into the oven and bake for 17-22 minutes, or until golden brown. Remove from the oven and let it cool on a rack before slicing and serving.