7. If the coordinates of the two foci of an ellipse are $(-1,0)$ and $(1,0)$, and the equation of a tangent line is $x+y=7$, then the eccentricity of the ellipse is $\qquad$

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7. $\frac{1}{5}$.

Let the equation of the ellipse be $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, where $a>b>0$. It is easy to know that $a^{2}=b^{2}+1$. The equation of the tangent line to the ellipse at the point $(a \cos t, b \sin t)$ is
$$
\frac{x \cos t}{a}+\frac{y \sin t}{b}=1 .
$$

By comparing with the given tangent line equation, we know that $a=7 \cos t, b=7 \sin t$, i.e., $a^{2}+b^{2}=49$. Thus, $a^{2}=25, b^{2}=24$. Therefore, the eccentricity of the ellipse is $\frac{1}{5}$.