Know if value is in array without equality comparison!

First of all, by taking the cout this code is C and not C ++, almost everyone learns to do C ++ the wrong way. And if doing it in C ++ would be as simple as PHP, you would just use a ready function, like find() for example. But if you want the hard way would be:

#include <iostream>
using namespace std;

int main () {
    int e[5] = {10, 20, 30, 40, 50};       
    for (int i = 0; i < 100; i++) {
        for (int j = 0; j < 5; j++) {
            if (e[j] == i) {
                cout << i;
                break;
            }
        }
    }
}

See running on ideone . And no Coding Ground . Also I placed GitHub for future reference .

Or if that's the case (and the way it does in PHP is bad) you can do it in a smarter and more performative way:

#include <iostream>
using namespace std;

int main () {
    int e[5] = {10, 20, 30, 40, 50};       
    for (int i = 0; i < 5; i++) if (e[i] >= 0 && e[i] < 100) cout << i;
}

See running on ideone . And no Coding Ground . Also I put it in GitHub for future reference .

Complementing what @Maniero already said, you can use the std::find that is part of the algorithms library to search if the element exists. The find receives 3 values, the initial, final element, and the value to be searched.

Transposing this to your code would look like this:

#include <iostream>
#include <algorithm> // inclusão do header associado
using namespace std;

int main (void){

       int e[5] = {10,20,30,40,50};       

       for (int i = 0; i <= 99; i++){
            if (find(e, e + 5, i) != e + 5) cout << i << " "; 
            //   ^---^----^----^---- utilização do find
       }
}

See this example in Ideone

In this example the initial value was set by the pointer to the first element with e , and the end set also with a pointer, but advancing the amount of elements sufficient to be next to the last, e + 5 .

As find returns a pointer to the found element, or to the end if there is no equal element, you must compare if that pointer is at the end.

A more natural use of this language is to save the search result to a pointer / iterator and then use it when you want to access the found element:

for (int i = 0; i <= 99; i++){
    int *pesq = find(e, e + 5, i);
    if (pesq != e + 5) cout << *pesq << " ";
    //                           ^--- imprime o valor encontrado com base no ponteiro devolvido

}

See this example also in Ideone

As indicated by @MarioFeroldi in comment, you can also use std::begin and std::end to get the start and end of a normal array. This makes the code more flexible because it only defines the size in a location:

int e[5] = {10,20,30,40,50};       

for (int i = 0; i <= 99; i++){
    int *pesq = find(begin(e), end(e), i);
    //                 ^--------^
    if (pesq != end(e)) cout << *pesq << " ";
    //           ^---
}

See it on Ideone

#include <iostream>
#include <algorithm>
#include <vector> //vector também necessário agora

using namespace std;

int main (void){

       vector<int> e = {10,20,30,40,50};       

       for (int i = 0; i <= 99; i++){
            if (find(e.begin(), e.end(), i) != e.end()) cout << i << " "; 
       }
}

Example on Ideone

Now the start and end of the search was built based on the method begin and end of vector that return iterators to the corresponding elements.

Note: The code examples given in this answer have been adapted from documentation