Cook and drain the pasta according to package directions for al dente.
Place the eggs into a large pot and cover them with 1 inch of cold water. Bring to a boil. Turn off the heat and cover for 12 minutes. Remove the eggs into a bowl of ice water. Once the eggs are cool, remove them from the water onto a paper towel.
Peel the eggs and give them a rough chop. Dice the celery and the onion.
In a large bowl, whisk together the mayonnaise, mustard, paprika, salt, pepper, horseradish and relish.
Fold in the cooked macaroni, eggs, celery and onion.