I would like to say that regardless of the algorithm selection requirements, this is a primary school math problem of finding .
When inputting, check whether a and b are both odd or even numbers and whether the number is within the available range of the super variable type, and then you must also consider this issue in the case you generate

import java.math.BigInteger;
import java.util.*;
import java.io.*;
 
public class Main {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
 
        String total, more;
        for(int t = 0; t < 10; ++t) {
            total = input.nextLine();
            more = input.nextLine();;
            BigInteger total_apples = new BigInteger(total);
            BigInteger excess_apples = new BigInteger(more);
 
            BigInteger ans_1 = total_apples.add(excess_apples).pide(BigInteger.valueOf(2));
            BigInteger ans_2 = total_apples.subtract(excess_apples).pide(BigInteger.valueOf(2));
 
 
 
            System.out.println(ans_1);
            System.out.println(ans_2);
 
        }
    }
}

Using the materials you provided, I coded it in C++ as follows. I hope you can correct me!

/*
  if Natalia's number of apples is x  (x>0)
  apples:the number of apple
  extra:the number that Klaudia more tha Natalia
  (apples>extra>0)
  so
  x+extra+x=apples
  x = (apples-extra)/2
*/
#include <iostream>
int main(int argc, char const *argv[]) {
  int apples,extra;   //apples:the number of apple  extra:the number that Klaudia more tha Natalia

  for (size_t i = 0; i < 10; i++) {
        std::cin>>apples>>extra;   //input
        try{
          //To determine whether the input is legal
            if(apples<=0 || extra<=0 || apples<extra || (apples-extra)%2!=0) throw apples;
            int Klaudia,Natalia;
            Natalia = (apples-extra)/2;    //calculate
            Klaudia=Natalia+2;
            std::cout<<Klaudia<<'\n'<<Natalia<<'\n';    //output
      }
        catch(int e){
            //ERROR
            std::cerr << "ERROR! the number of applse is error.\n" << '\n';
        }
  }
  return 0;
}

Run results