What means this " ` " Symbol ?
Is a numeric value with MachinePrecision see for more info.
With correct syntax:
$Version
(* "12.0.0 for Microsoft Windows (64-bit) (April 6, 2019)" *)
ClearAll["Global`*"]
Tx = 68.4; T9 = 25.4; T1 = 90; L = 0.35; x = 0.05;
NSolve[(Tx - T9)/(T1 - T9) == Cosh[m (L - x)]/Cosh[m L], m, Reals]
(*{{m -> -8.22068}, {m -> 8.22068}}*)
Solve[(Tx - T9)/(T1 - T9) == Cosh[m (L - x)]/Cosh[m L], m, Reals]
{{m -> -8.22068}, {m -> 8.22068}}
Solve gives a error message because Solve command works better with exact values.
ClearAll["Global`*"]
Tx = 684/10; T9 = 254/10; T1 = 90; L = 35/100; x = 5/100;
Solve[(Tx - T9)/(T1 - T9) == Cosh[m (L - x)]/Cosh[m L], m, Reals]
%//N
(*{{m -> -8.22068}, {m -> 8.22068}}*)
ClearAll["Global`*"]
Solve[(Tx - T9)/(T1 - T9) == Cosh[m (L - x)]/Cosh[m L], m, Reals]
(*General solution is impossible*)