Alice’s age in years is twice Eve’s age in years. In $10$ years, Eve will be as old as Alice is now. Compute Alice’s age in years now.
1. Denote Alice's age as \( a \) and Eve's age as \( b \).
2. From the problem statement, we have the following system of equations:
   \[
   a = 2b \quad \text{(Alice's age is twice Eve's age)}
   \]
   \[
   a = b + 10 \quad \text{(In 10 years, Eve will be as old as Alice is now)}
   \]
3. We can equate the two expressions for \( a \):
   \[
   2b = b + 10
   \]
4. Solve for \( b \):
   \[
   2b - b = 10
   \]
   \[
   b = 10
   \]
5. Substitute \( b = 10 \) back into the equation \( a = 2b \):
   \[
   a = 2 \times 10 = 20
   \]

The final answer is \(\boxed{20}\).