The TAJE226K035RNJ is a 22 µF, 35 V rated tantalum capacitor in the TAJ series from KYOCERA AVX, molded case, surface-mount in the 2917 (7343 Metric) footprint. The 500 mOhm ESR is the series resistance that limits ripple current and sets the self-heating under AC load — for a 12 V rail with 100 mV ripple, this ESR keeps the ripple current under 200 mA, which is within the capacitor's safe operating area at 85°C.
At 125°C the voltage derating is typically 50% — the 35 V rating drops to 17.5 V, so a 12 V rail at 125°C has 5.5 V of margin. The ±10% tolerance means the actual capacitance at 25°C is between 19.8 µF and 24.2 µF; at -55°C the capacitance falls by about 10% from the 25°C value, so the minimum is roughly 17.8 µF.