= Solution
In a <Grothendieck topos> define
$$
\Delta S=\coprod_{s\in S}1,\qquad
\Gamma A=\operatorname{Hom}_{\mathcal E}(1,A).
$$
The <coproduct> universal property gives $\operatorname{Hom}_{\mathcal E}(\Delta S,A)\cong\operatorname{Set}(S,\Gamma A)$, naturally. Thus $\Delta\dashv\Gamma$. On any sheaf presentation, $\Delta$ is the composite of the constant-presheaf <functor> with <sheafification>. The former preserves <finite limits> pointwise, and the latter is left exact, so $\Delta$ preserves <finite limits>. Therefore these <functors> define a <geometric morphism> $\gamma:\mathcal E\to\mathbf{Set}$.
For uniqueness, let $v$ be any such <geometric morphism>. Its inverse image is a <left adjoint> and preserves the <terminal object>. Every set has the canonical <coproduct> decomposition $S=\coprod_{s\in S}\{*\}$, so
$$
v^*S\cong\coprod_{s\in S}v^*\{*\}
\cong\coprod_{s\in S}1=\Delta S.
$$
These isomorphisms respect all functions between sets, giving a <natural isomorphism> $v^*\cong\Delta$. The <right adjoint> is then unique up to the corresponding <natural isomorphism>, so $v_*\cong\Gamma$. \b[There is a unique <geometric morphism> to sets, up to isomorphism], called the <global sections geometric morphism>. This also applies to the degenerate topos.
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