Step 1: Understand the test.
We are detecting an extra element E in an organic compound. The clue is that the final test uses ammonium molybdate and gives a yellow precipitate.
Step 2: Recall the yellow precipitate test.
A yellow precipitate with ammonium molybdate is the classic confirming test for phosphorus, present as phosphate.
Step 3: Follow the first reaction.
Heating the organic compound with sodium peroxide oxidises the phosphorus into phosphate ions, which become sodium phosphate.
Step 4: Follow the acid step.
Boiling with nitric acid turns the phosphate into phosphoric acid in an acidic medium, ready for the next test.
Step 5: Form the yellow precipitate.
Phosphoric acid then reacts with ammonium molybdate to give a canary-yellow precipitate of ammonium phosphomolybdate. \[ H_3PO_4 + 12(NH_4)_2MoO_4 + 21HNO_3 \longrightarrow (NH_4)_3PO_4{\cdot}12MoO_3 \downarrow + \ldots \]
Step 6: Identify E.
This yellow precipitate confirms the element is phosphorus. \[ \boxed{E = P} \]