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A 19-year-old woman was admitted to the Department of Dermatology due to gen­eralized red scaly patches on the skin and short, dry, spiky hair. The patient reported coexisted itch. The lesions persisted from the birth. Gastroesophageal reflux and blood-mixed mucoid stool at the age of three months were observed. Allergy to cow’s milk, egg, peanuts and soya was diagnosed. The patient was previously treated with topical corticosteroids and pimecrolimus with no significant improve­ment. The parents of the patients were healthy and unrelated.

A physical examination revealed erythroderma with coexisted scaling. Moreover, sparse and short brittle hair were observed. On trichoscopy, trichorrhexis invaginata, matchstick and golf tee hairs were detected.

Laboratory tests revealed eosinophilia (4.24 × 103/ml with normal range 0–0.5 × 103/ml) and increased IgE level (2500 IU/ml with normal range: 0–100 IU/ml).

Based on the case description and the photographs, what is your diagnosis?