She'll recover from her illness soon.

Literal

[topic-は] before-long illness [from-から] will-recover probably.

回復する ('recover, regain [from a setback]') is a Sino-Japanese verb at home in formal/medical register — it covers recovery from illness, exhaustion, financial slump, or psychological distress. 病気から回復する ('recover from illness') uses から ('from') to mark the state being escaped/transcended. The native counterpart 治る ('heal,' intransitive) frames recovery from the illness's perspective ('the illness heals'); 回復する is more abstract and clinical, treating the person as the agent of recovery. 退院する ('be discharged from hospital') is yet another framing — the institutional event of leaving hospital care.