Section 42E. An owner of real estate aggrieved by a charge imposed thereon under sections forty-two A to forty-two F, inclusive, in addition to such remedy as he may have under section ten of chapter one hundred and sixty-five, may apply for an abatement thereof by filing a petition with the board or officer having control of the water department within the time allowed by law for filing an application for abatement of the tax of which such charge is, or, if the property were not tax exempt, would have been, a part, and if such board or officer finds that such charge is more than is properly due, a reasonable abatement shall be made; and except as otherwise provided herein, the provisions of chapter fifty-nine relative to the abatement of taxes by assessors shall apply, so far as applicable, to abatements hereunder. If such petition is denied in whole or in part, the petitioner may appeal to the appellate tax board upon the same terms and conditions as a person aggrieved by the refusal of the assessors of a city or town to abate a tax.