This is a browning reaction called Maillard browning. There is a small amount of carbohydrates in egg whites which are linked to the proteins. At high temperatures the carbohydrates react with amino acids in proteins to form the browning compounds. Its the same reaction that happens in baking...
The tan color is from overcooking the eggs. Egg whites have about 1% simple sugars attached to the protein. When eggs are cooked at too high of temperature, a browning reaction occurs, known as Maillard browning. It's rarely seen in hard cooked eggs but can happen. When you fry eggs in a...