Sure can! Here's a C++ version of the function and an example of how to use it:

```cpp
#include <iostream>
#include <vector>
#include <cmath>

double distance(const std::vector<double>& vector1, const std::vector<double>& vector2) {
    // Check if both vectors have the same dimension
    if (vector1.size() != vector2.size()) {
        return -1;
    }

    // Calculate the sum of squared differences between each element in the vectors
    double sum_of_squares = 0.0;
    for (int i = 0; i < vector1.size(); ++i) {
        double difference = vector1[i] - vector2[i];
        sum_of_squares += pow(difference, 2);
    }

    // Return the square root of the sum of squared differences
    return sqrt(sum_of_squares);
}

// Example usage
int main() {
    std::vector<double> v1 = {1, 2, 3};
    std::vector<double> v2 = {4, 5, 6};
    double dist = distance(v1, v2);
    std::cout << "Distance between v1 and v2: " << dist << std::endl;

    return 0;
}
```

Rather than returning `None`, this version returns a value of `-1` due to the need for strict typing in C++. You can compile it with the following command line command:

`g++ -std=c++11 distance.cpp -o program`

And you can run it with:

`./program`

Note that on Windows, you will want to name it `program.exe` instead.
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