Preheat oven to 350 degrees F (175 degrees C). Grease and flour two 9x5-inch loaf pans.

Mix tomatoes, sugar, walnuts, canola oil, eggs, vanilla extract, and salt together in a large bowl until well blended. Mix flour, cinnamon, baking soda, and baking powder together in a separate bowl; stir into egg mixture until just blended. Spoon batter into prepared loaf pans.

Bake in the preheated oven until a toothpick inserted in the middle of each loaf comes out clean, about 1 hour. Let cool in the pans for about 10 minutes before transferring loaves to wire racks to cool completely.