Whisk together flour, curry powder, brown sugar, granulated sugar, baking powder, red pepper, cumin, and paprika in a large bowl; stir eggs into dry ingredients to make thick batter; add sweet potatoes and salt and black pepper to taste, mix well Heat oil in a large, heavy skillet over medium-high heat; drop enough batter into hot oil to form 4-inch latkes when pressed down, do not crowd skillet.
Fry in batches until golden, about 4 minutes per side.