The KKT condition is given by introducing relaxation parameters to the objective (derivative equals 0) so that whenever any element of $x$ is above $0$ or below $u$, parameters can increase to allow the system of equations to satisfy but at the same time cause penalties when x is not optimal.

So we have the following linear system that needs to be solved.
$$
M=\begin{bmatrix}
Q & E^\mathrm{T} & -I & I \\
E & 0 & 0 & 0\\
I & 0 & 0 & 0\\
I & 0 & 0 & 0\\
\end{bmatrix}
\begin{bmatrix}
x \\
\lambda \\
\mu \\
h \\
\end{bmatrix}=\begin{bmatrix}
-q\\
b\\
0\\
u\\
\end{bmatrix}
$$

The KKT conditions are then the above equation for stationary, and complementary slackness (last two rows).
Your listed conditions for primal feasibility.
And $\lambda\ge0,\ \mu\ge0,\ h\ge0$ for dual feasibility.

This is my first ever answer on here. Hope I don't make a mistake.