The Board of Appeals shall have no power to amend this chapter or the Building Zone Map, but where there are practical difficulties or unnecessary hardships in the way of carrying out the provisions of this chapter, such Board, after due notice and public hearing, may prescribe, in a specific case, a variation in the application of any such provision, in harmony with the general purpose and intent of this chapter, so that the public health, safety and welfare may be conserved. The Board of Appeals shall have general power of review of any decision rendered by the Code Enforcement Officer.