Whenever there is a vacancy in either house of the General Assembly, by reason of failure to elect, ineligibility, death, resignation or otherwise, within 10 days of the creation of the vacancy a writ of election shall be issued by the presiding officer of the house in which the vacancy exists, directed to the Department or, in case of necessity, in such other manner as shall be provided by law. Whenever there is such vacancy in either house and the General Assembly is not in session, the Governor may issue a writ of election to fill such vacancy, which writ shall be executed as a writ issued by the presiding officer of either house in case of vacancy.