Solve [M*S + (T/0.755) - (T/0.755)*cosh[M/(2T/0.755)] == 0, T]

eqn = M S+(T/0.755)-(T/0.755)*Cosh[M/(2T/0.755)]==0;

seqn = Assuming[M>0, eqn /. T->t M //Simplify];
seqn //TeXForm

ode = D[seqn /. t->t[S], S];
ode //TeXForm

t1 = t /. First @ Solve[seqn && 0<t<10 /. S->1, t]

sol = NDSolveValue[{ode, t[1] == t1}, t, {S, 0, 10}];

Plot[sol[t], {t, 0, 10}]

Tsol[s_, m_] := m sol[s]

Plot3D[eqn[[1]] /. T->Tsol[S, M], {S, 0, 10}, {M, 0, 10}]