Rinse cucumber, cut in half lengthwise, cut diagonally into narrow slices. Place in a suitable bowl, season with salt. After cooling for about 10 minutes, rinse and drain. Remove peel from potatoes and carrots. Cut both diagonally into 3 mm thick slices. Remove peel from onions, cut into wedges.
Heat oil in a saucepan, sauté vegetables (except cucumber) briefly. Douse with clear soup, add rice vinegar and sugar and cook al dente for about 8 minutes. Drain in a sieve.
Mix eggs in a cup, mix with vegetables and cucumber and cook in a saucepan at low temperature. Season to taste with salt and freshly ground pepper.