Yes! The diagonals of a rhombus are at right angles.
So imagine a triangle whose base is the base of the rhombus, but whose apex is the middle, then use Pythagoras Theorem
a2 + b2 = c2
Remember, these are going to be half-diagonals, so the difference will only be 2, and lets call the short diagonal "x":
x2 + (x+2)2 = 102
x2 + x2 + 4x + 22 = 102
2x2 + 4x + 4 = 100
2x2 + 4x -96 = 0
This is a Quadratic Equation and the solutions are 6 and -8. The lengths won't be negative so "6" is the answer.
That is the short "half-diagonal", so the full diagonal will be 12, and the longer diagonal 16.
The area will be ½ × 12 × 16 = 96 (because you can calculate the area of a rhombus by multiplying the diagonals and then halving)