Whisk together tangerine juice, tangerine zest, sea salt, and olive oil.
Rinse and dry arugula and red butterhead lettuce. Put in a serving bowl and toss gently but thoroughly with only enough dressing to coat.
Add tangerines and croutons; toss just to mix. Divide salad among plates (or serve on a platter if you like). Add a quartered hard-cooked egg to each plate and drizzle eggs with a little more dressing.