Answer: E

Small Hint:

The oil surface is a rectangle of length $10$, so its width is $4$

Big Hint:

In the circular end, a chord of length $4$ lies $\sqrt{3^2-2^2}$ from the center

Solution:

The rectangular surface has length $10,$ so its chord width in the circular cross-section is $\frac{40}{10}=4.$ Half the chord is $2,$ and the radius is $3,$ so the distance from the center to the chord is $$\sqrt{3^2-2^2}=\sqrt5.$$ A chord of this length can lie either below or above the center. Measured from the bottom of the tank, the corresponding depths are $3-\sqrt5$ and $3+\sqrt5.$

Thus, the correct answer is E.