In 1978, motivated by E. Hückel's work in quantum chemistry, I. Gutman introduced the concept of the energy of a finite simple graph $G$ as the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$. At the time of writing, the MathSciNet search for "Title=(graph energy) AND Review Text=(eigenvalue)" returns 365 publications, most of which going after Gutman's definition. A congruence $\alpha$ of a finite algebra $A$ turns $A$ into a simple graph: we connect $x \neq y \in A$ by an edge iff $(x,y) \in \alpha$; we let $\textup{En}(\alpha)$ be the energy of this graph. We introduce the congruence energy $\textup{CE}(A)$ of $A$ by $\textup{CE}(A) := \sum\{\textup{En}(\alpha) : \alpha \in \textup{Con}(A)\}$. Let $\textup{LAT}(n)$ and $\textup{CDA}(n)$ stand for the class of $n$-element lattices and that of $n$-element congruence distributive algebras of any type. For a class $\mathcal{X}$, let $\textup{CE}(\mathcal{X}) := \{\textup{CE}(A) : A \in \mathcal{X}\}$. We prove the following: (1) For $\alpha \in \textup{Con}(A)$, $\textup{En}(\alpha)/2$ is the height of $\alpha$ in the equivalence lattice of $A$. (2) The largest number and the second largest number in $\textup{CE}(\textup{LAT}(n))$ are $(n-1) \cdot 2^{n-1}$ and, for $n \geq 4$, $(n-1) \cdot 2^{n-2} + 2^{n-3}$; these numbers are only witnessed by chains and lattices with exactly one two-element antichain, respectively. (3) The largest number in $\textup{CE}(\textup{CDA}(n))$ is also $(n-1) \cdot 2^{n-1}$, and if $\textup{CE}(A) = (n-1) \cdot 2^{n-1}$ for an $A \in \textup{CDA}(n)$, then $\textup{Con}(A)$ is a boolean lattice with size $|\textup{Con}(A)| = 2^{n-1}$.