In a large bowl, combine the carrots, radishes, and salt. Using your hands, gently massage the carrots and radishes until they start to soften, about 4-5 minutes.
In a small saucepan, stir together the water, vinegar, and sugar. Bring to a boil over medium-high heat and cook, stirring often, until the sugar has dissolved, 2-3 minutes.
Transfer the vegetables to a 1-quart glass jar and slowly pour the warm vinegar mixture into the jar. Allow the mixture to cool slightly, 30 minutes.
Seal the jar and let the vegetables pickle, refrigerated, for at least 1 hour before using, preferably overnight. Store refrigerated for up to 3 weeks.
