这是一坨屎山的字符串解法，回头会完善出来有注释的版本，先传上来orz

import java.util.Scanner;

public class P566 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String num1 = sc.nextLine();
        String num2 = sc.nextLine();
        boolean positiveNum1 = num1.charAt(0) != '-';
        boolean positiveNum2 = num2.charAt(0) != '-';
        num1 = RemoveSymbol(num1,positiveNum1);
        num2 = RemoveSymbol(num2,positiveNum2);


        if(num1.length() > num2.length())
        {
            int count = num1.length() - num2.length();
            for(int i = 0;i < count;i++)
            {
                num2 = "0" + num2;
            }
        } else if (num1.length() < num2.length()) {
            int count = num2.length() - num1.length();
            for(int i = 0;i < count;i++)
            {
                num1 = "0" + num1;
            }
        }


        String aws = "";
        if(positiveNum1 ^ positiveNum2){
            aws = SubtractionOperation(num1,num2,positiveNum1);

        }else {
            aws = AdditionOperation(num1,num2);
            if(!positiveNum1 && aws.charAt(0)!='0'){
                aws = "-"+aws;
            }
        }


        if(aws.isEmpty())
        {
            aws = "0";
        }
        System.out.println(aws);
    }

    public static String RemoveSymbol(String num,boolean positiveNum){
        if(!positiveNum){
            num = num.substring(1);
        }
        return num;
    }
    public static String AdditionOperation(String num1,String num2){
        String aws = "";
        boolean judge = false;
        for(int i = num1.length()-1;i >= 0;i--)
        {

            int a = num1.charAt(i)-48;
            int b = num2.charAt(i)-48;

            int sum = a + b;

            if(judge)
            {
                sum++;
                judge = false;
            }

            if(sum >= 10)
            {
                sum = sum%10;
                judge = true;
            }
            aws = sum + aws;
            if(i == 0 && judge)
            {
                aws = "1" + aws;
            }
        }
        return aws;
    }
    public static String SubtractionOperation(String num1,String num2,boolean positiveNum1){
        String aws = "";
        String temp;
        if(!positiveNum1){
            temp = num1;
            num1 = num2;
            num2 = temp;
        }
        boolean judge = false;
        boolean isNegative  = false;
        for(int i = num1.length()-1;i >= 0;i--)
        {

            int a = num1.charAt(i)-48;
            int b = num2.charAt(i)-48;

            int sub = a - b;

            if(judge)
            {
                sub--;
                judge = false;
            }

            if(sub < 0)
            {
                boolean isEnd = true;
                for (int j = i - 1; j >= 0 ; j--) {
                    if(num1.charAt(j) != '0'){
                        isEnd = false;
                        break;
                    }
                }
                if(isEnd){
                    sub = -sub;
                    if(i == 0){
                        judge = true;
                    }
                }else {
                    sub += 10;
                    judge = true;
                }

            }
            aws = sub + aws;
            if(i == 0 && judge)
            {
                isNegative = true;
            }
        }
        aws = RemoveExtraZero(aws);
        if(isNegative){
            aws = "-"+aws;
        }
        return aws;
    }
    public static String RemoveExtraZero(String aws){
        String aws2 = "";
        boolean judge2 = true;
        for(int i = 0;i < aws.length();i++) {
            if(aws.charAt(i) == '0' && judge2)
            {
                continue;
            }
            else if(aws.charAt(i) != '0')
            {
                judge2 = false;
            }
            aws2 += aws.charAt(i);
        }
        return aws2;
    }

加法运算

方法一:用字符串截取计算，逻辑复杂一些

方法二:用bigInteger

Scanner sc=new Scanner(System.in);

String a=sc.next();

String b=sc.next();

BigInteger a1=new BigInteger(a);

BigInteger b1=new BigInteger(b);

String ans=a1.add(b1).toString();

System.out.println(ans);