The Brouwer's toughness conjecture states that every $d$-regular connected graph always has $t(G)>\frac{d}λ-1$ where $λ$ is the second largest absolute eigenvalue of the adjacency matrix. In 1988, Enomoto introduced a variation of toughness $τ(G)$ of a graph $G$. By incorporating the variation of toughness and spectral conditions, we provide spectral conditions for a graph to be $τ$-tough ($τ\geq 2$ is an integer) and to be $τ$-tough ($\frac{1}τ$ is a positive integer) with minimum degree $δ$, respectively. Additionally, we also investigate a analogous problem concerning balanced bipartite graphs.