方法一 拆分字符串相加

import java.util.Scanner;
import java.math.BigInteger;
import java.util.Stack;

// 注意类名必须为 Main, 不要有任何 package xxx 信息
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        // 注意 hasNext 和 hasNextLine 的区别
            String Str1 = in.nextLine();
            String Str2 = in.nextLine();
            System.out.println(addNumber(Str1, Str2));
    }
    public static String addNumber(String str1, String str2) {
        int str1Length = str1.length() - 1;
        int str2Length = str2.length() - 1;
        int carry = 0;
        Stack<Integer> stack = new Stack<>();
        while (str1Length >= 0 || str2Length >= 0 || carry == 1) {
              int temp = 0;
              if (str1Length >= 0 && str2Length >= 0) {
                  temp = carry + str1.charAt(str1Length) - '0' + str2.charAt(str2Length) - '0';
                  str1Length = str1Length - 1;
                  str2Length = str2Length - 1;
              } else if (str1Length >= 0 && str2Length < 0) {
                  temp =  carry + str1.charAt(str1Length) - '0';
                  str1Length = str1Length - 1;
              } else if (str2Length >= 0 && str1Length < 0) {
                  temp = carry + str2.charAt(str2Length) - '0';
                  str2Length = str2Length - 1;
              } else {
                  temp = carry;
              }
              carry = temp / 10;
              stack.push(temp % 10);
        }
        StringBuffer sb = new StringBuffer();
        while (!stack.isEmpty()) {
           sb.append(stack.pop());
        }
        return sb.toString();
    }
}

方法二 使用BigInteger类,相加

import java.util.Scanner;
import java.math.BigInteger;

// 注意类名必须为 Main, 不要有任何 package xxx 信息
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        // 注意 hasNext 和 hasNextLine 的区别
            BigInteger a = in.nextBigInteger();
            BigInteger b = in.nextBigInteger();
            System.out.println(a.add(b));
    }
}