What is the ruling on a woman's work that involves her intermingling with men in a public office, in the presence of other employees?

It is not permissible for a woman to work in a place where there is direct mixing with men and no distinction between them, unless there is a clear distinction, safety from temptation, and avoidance of seclusion (khalwa) and speaking softly. The fundamental principle is for a woman to remain in her home, except out of necessity.