ICP measures total elemental content from dissolved samples with high sensitivity, while EDS analyzes surface composition with lower sensitivity and limited depth, causing differences. Their different sample states and detection limits are the main reasons for conflicting results.
What do you mean by "conflict"? Are the concentrations of your elements of interest markedly different, or are they within the measurement of uncertainty of the other technique?
Along with Abdelhak Maghchiche 's answer, are you accounting for the oxide component of the EDS measurements?
Also, what is the experimental system you are measuring? If it is a sample of a tiny archaeological artifact that cannot be duplicated for example, you will want to be as accurate as you can (microgram or nanogram accuracy), with a single measurement, whereas, if it is a product made in 1000 kg batches, you can probably cope with a few percentage points of measurement error.
ICP provides highly sensitive bulk elemental analysis from dissolved samples, while EDS gives surface composition with lower sensitivity and limited depth, often leading to differences in results. These discrepancies arise mainly from different sample states, detection limits, and the presence of surface oxides in EDS measurements.
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