Given information:
- Point P has coordinates (2, -3).
- Point Q has coordinates (10, y).
- The distance between points P and Q is 10 units.

Formula for calculating distance between two points:
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

Applying the formula:
Let's apply the distance formula to calculate the distance between points P and Q:

d = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(10 - 2)^2 + (y - (-3))^2]
= √[8^2 + (y + 3)^2]
= √[64 + (y + 3)^2]
= √(64 + y^2 + 6y + 9)
= √(y^2 + 6y + 73)

Since the distance between P and Q is given as 10 units, we can set up the equation:

√(y^2 + 6y + 73) = 10

Solving for y:
To solve this equation, we need to isolate y. Squaring both sides of the equation will help us eliminate the square root:

(y^2 + 6y + 73) = 10^2
y^2 + 6y + 73 = 100
y^2 + 6y + 73 - 100 = 0
y^2 + 6y - 27 = 0

Now we can solve this quadratic equation for y using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

For our quadratic equation y^2 + 6y - 27 = 0, the values of a, b, and c are:
a = 1
b = 6
c = -27

Substituting these values into the quadratic formula, we get:

y = (-(6) ± √((6)^2 - 4(1)(-27))) / (2(1))
y = (-6 ± √(36 + 108)) / 2
y = (-6 ± √144) / 2
y = (-6 ± 12) / 2

Now we have two possibilities for y:

1. y = (-6 + 12) / 2 = 6 / 2 = 3
2. y = (-6 - 12) / 2 = -18 / 2 = -9

Therefore, there are two values of y for which the distance between points P(2, -3) and Q(10, y) is 10 units: y = 3 and y = -9.