What do you mean by
"Then, if the energy is $E_1+\Delta E$"
? The energy of what? If you mean the measured energy, then it is impossible, since the measured energy can be just one of the allowed energies, in this case $E_1$ or $E_2$. If you mean the expected value of the energy before the measurement, then your conclusion is wrong, and I'll try to explain why.
First of all, you didn't define what you mean by uncertainty, so I'll assume that you are talking about the most used form for uncertainty in quantum mechanics - the standard deviation, which is what appears in the uncertainty principle.
There is no problem with the uncertainty being smaller than the energy difference between the discrete energy state.
First, to make sure you understand, the uncertainty is a result of the principle of superposition (whereas the uncertainty principle is a result of the non-orthogonality of eigenstates of different observables). If we speak about energy, then the uncertainty is zero if the particle (or whatever) is in an energy eigenstate of the system. But if the particle's state is a superposition of energy eigenstates, then the outcome of an energy measurement can be any of these energies, and therefore there is uncertainty in energy.
How much uncertainty? this depends on the coefficients of the superposition. The (squared modulus) of these coefficients are the probabilities to measure the corresponding energy (assuming for now that the energies are non-degenerate). Let's take an example with two energies, $E_1=0$ and $E_2=1$ (in whatever units you choose), and probabilities of $p$ for the first outcome and $1-p$ for the second. Then the expected value of the energy measurement is $pE_1+(1-p)E_2=1-p$. And the standard deviation is $\sqrt{p(1-p)}$. This standard deviation is the uncertainty we are talking about. And notice that it can take any value between $0$ (when $p=0$ or $p=1$) and $0.5$ (when $p=0.5$). Specifically, it can be very small, much smaller then the energy difference between $E_1$ and $E_2$. But for the difference to be very small, $p$ needs to be very close to $1$ or $0$. This means that with high certainty, the energy will be $E_1$ (in the former case), but there is still a small chance to measure $E_2$. The small uncertainty indicates exactly this.
Bottom line: the correct conclusion to draw if the uncertainty $\Delta E$ is small compared to differences in the discrete energy spectrum, is that it is more likely for the measured energy to be one of the energies in the spectrum than others.