The board of adjustment shall have the following powers:
 1. To hear and decide appeals where it is alleged there is error in any order, requirement, decision or determination made by an administrative official in the enforcement of this chapter or of any ordinance adopted pursuant thereto.
 2. To hear and decide special exceptions to the terms of the ordinance upon which such board is required to pass under such ordinance.
 3. To authorize upon appeal, in specific cases, such variance from the terms of the ordinance as will not be contrary to the public interest, where owing to special conditions a literal enforcement of the provisions of the ordinance will result in unnecessary hardship, and so that the spirit of the ordinance shall be observed and substantial justice done.