Preheat the oven to 325 degrees F (165 degrees C). Grease two 8x4-inch loaf pans.

Whisk eggs together in a large bowl. Add pumpkin purée and vegetable oil; whisk until smooth.

Whisk flour, sugar, pudding mix, baking soda, cinnamon, and salt together in a separate bowl; stir into pumpkin mixture. Divide batter between the prepared loaf pans.

Bake in the preheated oven until a toothpick inserted into centers comes out clean, 75 to 80 minutes.