Robust tests (RW and RF) are provided for testing the equality of two long-tailed symmetric (LTS) means when the variances are unknown and arbitrary. RW test is a robust version of Welch's two sample t test and the RF is a robust fiducial based test. The RW and RF tests are proposed using the adaptive modified maximum likelihood (AMML) estimators derived by Tiku and Surucu (2009)