From the post "Torus", the quadratice equation has roots,
(Av2+n−1∑i=1q24εor2ei)r2e−mev2re+14{4nGmpme−TeTnπτo}=0
given by,
re=mev2±√(mev2)2−(Av2+n−1∑i=1q24εor2ei){4nGmpme−TeTnπτo}2(Av2+n−1∑i=1q24εor2ei)
For double root,
(mev2)2−(Av2+n−1∑i=1q24εor2ei){4nGmpme−TeTnπτo}=0
I have wanted to use silver again to estimate for τo, it seems the term,
n−1∑i=1q24εor2ei
is inaccessible.