The Board of Adjustment shall have the power to vary the regulations of any district so as to relieve difficulties or hardships in cases when and where, by reason of exceptional narrowness, shallowness, or shape of a specific piece of property at the time of the enactment of such regulation or restriction, or by reason of exceptional topographical conditions or other extraordinary and exceptional situations or conditions of such piece of property, the strict application of each regulation or restriction would result in peculiar and exceptional practical difficulties to, or exceptional hardship upon, the owner of such property. Such grant or variance shall comply, as nearly as possible, in every respect with the spirit, intent, and purposes of the zoning plan, it being the purpose of provision to authorize the granting of variation only for reasons of demonstrable and exceptional hardship as distinguished from variation sought by applicants for purposes or reasons of convenience, profit or caprice.