The Zoning Board of Appeals may authorize upon appeal, or upon petition in cases where dimensional modifications are sought with respect to a particular parcel of land or to an existing building thereon, a variance from the terms of this chapter, where, owing to conditions specifically affecting each parcel or such building, but not affecting generally the zoning district in which it is located, a literal enforcement of the provisions of this chapter would involve substantial hardship, financial or otherwise, to the appellant and where desirable relief may be granted without nullifying or substantially derogating from the intent or purpose of this chapter, but not otherwise. The Zoning Board of Appeals shall hold a public hearing in accordance with the provisions of Chapter 40A on all variance applications brought before it.