In a small bowl, soak mushrooms in 1/2 cup hot water for 15 minutes. Drain and squeeze dry; reserve soaking liquid. Cut off and discard stems; slice caps thinly. In a small bowl, soak the tree ears (if using) in 1/2 cup hot water for 30 minutes. Drain and squeeze dry. Remove any hard spots, and roughly chop the tree ears. Discard the soaking liquid.
In a large saucepan, combine broth, 1 cup water, vinegar, and reserved mushroom liquid; bring to a boil over high heat. Add pork, mushrooms, tree ears, tofu, and bamboo shoots.
In a small bowl, whisk together the cornstarch and 3 tablespoons cold water. When soup returns to a boil, stir in cornstarch mixture, stirring constantly until soup is just thickened (about 30 seconds). Stir in egg, and remove from heat. Stir in the oil, white pepper, sugar, and scallions.