yup, there's a couple ways to do this, both based on the Pythagorean formula.

A^2+B^2=C^2

where C is the hypotenuse, A and B are the legs.

But, since the triangle is isosceles, A=B, so

2*A^2=C^2

substituting...

2*A^2 = (10)^2 = 100

A^2 = 50 = 25*2

A= 5*sqrt(2)

or, if you happen to know that the sides of a 45-45-90 triangle have the ratio 1:1:sqrt(2), you can jump straight to

A*sqrt(2) = 10

A = 10/sqrt(2) = 5*sqrt(2)