= Solution
For an ideal smooth homogeneous substrate in <thermodynamic equilibrium>, <Young's equation> is
$$
\boxed{\gamma_{SA}=\gamma_{SL}+\gamma_{LA}\cos\theta,}
$$
where $A$ denotes air, $S$ the solid, and $L$ the chosen liquid. It follows either by balancing tangential interfacial forces at the <contact line> or by varying the wetted area at fixed drop volume.
The dry Teflon–air <surface energy> is the same in the two measurements, so subtracting the two equations eliminates it:
$$
\gamma_{SW}-\gamma_{SO}
=\gamma_{OA}\cos\theta_O-\gamma_{WA}\cos\theta_W.
$$
Therefore
$$
\boxed{\gamma_{SW}-\gamma_{SO}
=23.8\cos25^\circ-72.8\cos102^\circ
\simeq36.7\,\mathrm{mN\,m^{-1}}=36.7\,\mathrm{mJ\,m^{-2}}.}
$$
The water–Teflon interface has the higher interfacial <free energy> per unit area. Neither individual solid–liquid <surface energy> is determined without the solid–air value; the difference is determined.
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