Cut the carrots and daikon into matchsticks about 1/4 inch thick and 2 inches long. Even cuts matter: uneven pieces pickle unevenly.
Toss the matchsticks with the kosher salt in a bowl and let stand 15 minutes. The vegetables will release water and soften slightly.
Rinse the salted vegetables under cold water and squeeze gently to remove excess liquid. Do not skip the rinse — unrinsed vegetables make an over-salted brine.
In a clean jar or bowl, stir the vinegar, water, and sugar until the sugar dissolves. (Some cooks heat the brine to dissolve the sugar faster; either works as long as it cools before the vegetables go in.)
Pack the vegetables into a clean glass jar and pour the cooled brine over to cover completely.
Refrigerate immediately. The pickles are ready after about 4 hours and are at their best within the first week.