Said board of appeals shall hear, determine, and decide appeals from and review any order, requirement, decision, or determination made by the administrative official charged by ordinance of any of said cities with the enforcement of any ordinance duly adopted pursuant to the provisions of the act, entitled “A supplement to an act, entitled ‘An act for the government of cities of the second class,’ approved the seventh day of March, one thousand nine hundred and one; authorizing cities of the second class to regulate and limit the height and bulk of buildings and the areas of yards, courts and open spaces, and to regulate and restrict the location of trades and industries, and the location of buildings for specified uses, and to make regulations for trades and industries and for the use of buildings; and, for the above purposes, to divide the cities into districts; and authorizing the city planning commission to recommend the boundaries of districts and appropriate regulations therein; and providing the method of adoption of said districts, regulations, and restrictions, and the method of amendment or change thereof,” approved June twenty-first, one thousand nine hundred and nineteen (Pamphlet Laws, five hundred and seventy),¹ and the supplements or amendments thereto; they shall also hear and decide all matters referred to them, and upon which they are required to pass, under any ordinance adopted pursuant to the provisions of said act, and its supplements or amendments. Such decisions may be made by the vote of the majority of said board. Such appeal shall be taken by any person aggrieved or by the head of any department of said city affected thereby or interested therein. Every decision of such board shall, however, be subject to review by appeal. The board of appeals may reverse or affirm, wholly or partly, or may modify the order, requirement, decision, or determination, as in its opinion ought to be made in the premises; and, to that end, shall have all the powers of the officer from whom the appeal is taken where there are practical difficulties or unnecessary hardships in the way of carrying out the strict letter of such ordinance. The board of appeals shall have the power in passing upon appeals to vary or modify any of the regulations or provisions of said ordinance in harmony with their general purpose and intent, and in accordance with general or specific rules therein contained, so that the spirit of the ordinance shall be observed; the public health, the public safety, and the general welfare, secured; and substantial justice done.