Preheat oven to 250°F.
Peel potatoes and coarsely grate by hand, transferring to a large bowl of cold water as grated. Soak potatoes 1 to 2 minutes after last batch is added to water, then drain well in a colander.
Spread grated potatoes and onion on a kitchen towel and roll up jelly-roll style. Twist towel tightly to wring out as much liquid as possible. Transfer potato mixture to a bowl and stir in egg and salt.
Heat 1/4 cup oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking. Working in batches of 4 latkes, spoon 2 tablespoons potato mixture per latke into skillet, spreading into 3-inch rounds with a fork. Reduce heat to moderate and cook until undersides are browned, about 5 minutes. Turn latkes over and cook until undersides are browned, about 5 minutes more. Transfer to paper towels to drain and season with salt. Add more oil to skillet as needed. Keep latkes warm on a wire rack set in a shallow baking pan in oven.