For practice purposes the while-loop that you have created makes sense, since it allows you to enter new data multiple times. But for this exercise, a loop is not foreseen, neither does it contain a breaking-condition to break the loop. Result => StackOverflow for judge :-(

Best,

using System;

namespace _3._Floating_Equality
{
    class Program
    {
        static void Main(string[] args)
        {
            double eps = 0.000001;
            double n1 = 0.0;
            double n2 = 0.0;
            
            // while (true)
            // {
                n1 = double.Parse(Console.ReadLine());
                n2 = double.Parse(Console.ReadLine());
                bool isEqual = Math.Abs(n1 - n2) < eps;

                if (isEqual)
                {
                    Console.WriteLine("True");
                }
                else
                {
                    Console.WriteLine("False");
                }
            // }
        }
    }
}

Както коментира колегата ти използваш безкраен цикъл,който не прекъсваш никъде.

Ето ти още един вариант:

using System;

namespace _3._Floating_Equality
{
    class Program
    {
        static void Main(string[] args)
        {
            double eps = 0.000001;
            double n1 = 0.0;
            double n2 = 0.0;
            
            while (true)
            {
                n1 = double.Parse(Console.ReadLine());
                n2 = double.Parse(Console.ReadLine());
                bool isEqual = Math.Abs(n1 - n2) < eps;

                if (isEqual)
                {
                    Console.WriteLine("True");

                    return;
                }
                else
                {
                    Console.WriteLine("False");

                    return;
                }               
            }
        }
    }
}

https://pastebin.com/riQz1Rjs

Ето едно по кратко решение от мен - https://pastebin.com/FXnbj1rx