The Commission may, upon motion therefor made within 10 days after service of a decision and order, order a rehearing before the Commission upon such terms and conditions as it may deem just and proper if a petition for judicial review of the decision and order has not been filed. Such motion shall not be granted except upon a showing that there is additional evidence which is material and necessary and reasonably calculated to change the decision of the Commission, and that sufficient reason existed for failure to present such evidence at the hearing of the Commission. The motion shall be supported by an affidavit of the moving party or counsel for the moving party showing with particularity the materiality and necessity of the additional evidence and the reason why it was not introduced at the hearing. Upon rehearing, rebuttal evidence to the additional evidence shall be permitted. After rehearing, the Commission may modify its decision and order as the additional evidence may warrant.