On appeal from either an adjudicatory order or rule-making decision, any interested party may submit a written brief, and the Board may request either the employee or the institution concerned or both to submit written briefs. The Board may, in its discretion, decide the appeal on the basis of such written briefs or it may request the parties to present oral argument. Either party may request the opportunity to present oral argument but, except as hereinafter provided, shall not have a right to be heard orally. The employee may be represented at any hearing or argument by legal counsel or other adviser. On appeal from an order dismissing a faculty member with tenure, or terminating during its term the appointment of a faculty member without tenure, the faculty member shall, on request, have a right to be heard orally.