What is the ruling on a woman working as a teacher in a school managed by a man, where most of the teaching staff are female, while employees are prohibited from covering their face and hands?

A woman is permitted to work as a teacher under the following conditions: She must wear the hijab (definition) and not use perfume; she must not be in seclusion with the principal or male teachers; she must not speak to non-mahram (definition) men unless there is a need, and without softening her voice; and she must teach either girls or boys who are not older than ten years of age. She must not uncover her face or hands in front of non-mahram men, even if this leads to her dismissal.