Let's denote the two numbers as $x$ and $y$. According to the problem, we have the following system of equations:

1. $x + y = 28$
2. $x \times y = 48$

We can solve this system by substitution or using a quadratic equation. Let's proceed with substitution:

From the first equation, solve for one variable, say $y$:

$y = 28 - x$

Substitute this into the second equation:

$x \times (28 - x) = 48$

Expand and simplify:

$28x - x^2 = 48$

Rearrange the terms to form a standard quadratic equation:

$x^2 - 28x + 48 = 0$

Now, solve this quadratic equation using the quadratic formula:

$x = \frac{-(-28) \pm \sqrt{(-28)^2 - 4(1)(48)}}{2(1)}$

Simplify the expression:

$x = \frac{28 \pm \sqrt{784 - 192}}{2}$

$x = \frac{28 \pm \sqrt{592}}{2}$

$x = \frac{28 \pm 24.33}{2}$

So, the two possible values for $x$ are:

$x = \frac{28 + 24.33}{2} = 26.165 \quad \text{or} \quad x = \frac{28 - 24.33}{2} = 1.835$

Thus, the two numbers are approximately $26.165$ and $1.835$.

Would you like further clarification on these steps or the calculation? Here are some related questions:

1. How do you solve a quadratic equation using the quadratic formula?
2. What are the different methods to solve systems of equations?
3. How can you check your solutions for problems involving sums and products?
4. What does the discriminant of a quadratic equation tell us?
5. How do you solve problems with two variables that involve both addition and multiplication?

Tip: When solving for two unknowns in such problems, make sure to check your final answer to see if both conditions (sum and product) are satisfied!