Sentinel loop won't run - c++

Question

My program will compile but I'm running into a couple problems. My first cout statement requiring e/E to end works, but in my second while loop where I state (+ || - || * || /) won't run. +/-/*// returns "Operation type invalid". Can you guys help me see my error?
First sentinel loop, just learning loops:
#include <iostream>
using namespace std;
int main()
{
int numOne;
int numTwo;
int result;
string operation;
cout << "Please enter what operation you'd like to perform or e/E to end program: ";
cin >> operation;
while (operation == "e" || "E")
{
cout << "Operation type invalid." << endl;
cout << "Please enter what operation you'd like to perform or e/E to end program: ";
cin >> operation;
}
while (operation == "+" || operation == "-" || operation == "*" || operation == "/")
{
cout << "Please enter integer one: " << endl;
cin >> numOne;
cout << "Please enter integer two: " << endl;
cin >> numTwo;
if (operation == "+")
{
result = numOne + numTwo;
cout << "The numbers you entered were " << numOne << "," << numTwo << endl;
cout << "The operation you chose was " << operation << "." << endl;
cout << "The operations result is " << result << "." << endl;
cout << "Your equation was: " << numOne << " " << operation << " " << numTwo << " = " << result << ".";
}
else if (operation == "-")
{
result = numOne - numTwo;
cout << "The numbers you entered were " << numOne << "," << numTwo << endl;
cout << "The operation you chose was " << operation << "." << endl;
cout << "The operations result is " << result << "." << endl;
cout << "Your equation was: " << numOne << " " << operation << " " << numTwo << " = " << result << ".";
}
else if (operation == "*")
{
result = numOne * numTwo;
cout << "The numbers you entered were " << numOne << "," << numTwo << endl;
cout << "The operation you chose was " << operation << "." << endl;
cout << "The operations result is " << result << endl;
cout << "Your equation was: " << numOne << " " << operation << " " << numTwo << " = " << result << ".";
}
else if (operation == "/")
{
if (numTwo == 0)
{
cout << "You cannot divide by zero!" << endl;
}
else
{
result = numOne / numTwo;
cout << "The numbers you entered were " << numOne << "," << numTwo << endl;
cout << "The operation you chose was " << operation << "." << endl;
cout << "The operations result is " << result << endl;
cout << "Your equation was: " << numOne << " " << operation << " " << numTwo << " = " << result << ".";
}
}
}
return 0;
}

Answer 1

while (operation == "e" || "E")
Here you are comparing one of two conditions:
Does operation == "e"?
If not, is "E" a valid pointer?
That second condition is your problem: "E" is of course a valid pointer, so that condition will always be true. Always. Notice that in the second condition, you are not comparing operation to "E".
You are forever stuck here:
while (operation == "e" || "E")
{
cout << "Operation type invalid." << endl;
cout << "Please enter what operation you'd like to perform or e/E to end program: ";
cin >> operation;
}
You simply need to have:
while (operation == "e" || operation == "E")
This is probably just a typo or an oversight more than anything else.