And one of those traditions is that the Ecumenical Councils spoke infallibly (a tradition we Orthodox agree with, though not with their theory that the papal assent was what made the councils both Ecumenical and infallible). The Fifth Ecumenical Council explicitly condemned the view that all will be saved (called the apokatastasis) among the heretical doctrines of Origen which were condemned.
We're allowed to pray for all to be saved (indeed some commentators on the Kneeling Prayers of Pentecost hold that on that one occasion the Church corporately prays not only for all the souls confined in Hades, but even for the demons), and even hope that it might be so, but to teach that it will or must be so is heresy. And this is a point on which our separated Latin brethren have traditionally agreed.